(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what is
the probability that any given letter will be in a given bucket?

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for the
prohibition that each letter may appear only once. In other words, are
there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

Thanks,

--Jeff

(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

You didn't give us enough information.  How do you decide which letters
go into which buckets?  

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

If the contents of the buckets are independent, the 5000 doesn't matter.
If they are not independent, it may.  

For example, one possible model is:
For each bucket, and each letter A to Z, with some given probability p
you put that letter in the bucket.  However, with probability (1-p)^26
this will leave 0 letters in the bucket.  In that case you start again.
The result is that each bucket contains a given letter with probability
p/(1 - (1-p)^26).

Another possible model:
For bucket #1, do as in the previous example.  Then, given bucket #i,
for bucket #(i+1) take a copy of bucket #i, remove one letter at random
and, if bucket #i had fewer than 13 letters, replace it with two letters
randomly chosen from those that are not in bucket #i.  
--
Robert Israel              isr...@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

On Jul 29, 2:57 pm, Robert Israel





isr...@math.MyUniversitysInitials.ca> wrote:
(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

You didn't give us enough information.  How do you decide which letters
go into which buckets?  

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

If the contents of the buckets are independent, the 5000 doesn't matter..
If they are not independent, it may.  

For example, one possible model is:
For each bucket, and each letter A to Z, with some given probability p
you put that letter in the bucket.  However, with probability (1-p)^26
this will leave 0 letters in the bucket.  In that case you start again.
The result is that each bucket contains a given letter with probability
p/(1 - (1-p)^26).

Another possible model:
For bucket #1, do as in the previous example.  Then, given bucket #i,
for bucket #(i+1) take a copy of bucket #i, remove one letter at random
and, if bucket #i had fewer than 13 letters, replace it with two letters
randomly chosen from those that are not in bucket #i.  
--
Robert Israel              isr...@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

Thanks for your reply, Professor.

Where I said "each letter may appear only once," I should have been
more clear and said "each letter may appear only once per bucket."

Also, let's indeed assume a uniform distribution--for our purposes
here,
"Z" is as likely as "E." So, among the 5000 buckets, each bucket
could
have A through Z, or anything in-between. In other words, letters go
into the buckets randomly.

The buckets are indeed independent of each other, so, from what you've
said,
the number of buckets is irrelevant.

-- Jeff

On Jul 29, 6:00 pm, jefftyzzer <jefftyz...@sbcglobal.net> wrote:



On Jul 29, 2:57 pm, Robert Israel

isr...@math.MyUniversitysInitials.ca> wrote:
(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

You didn't give us enough information.  How do you decide which letters
go into which buckets?  

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

If the contents of the buckets are independent, the 5000 doesn't matter.
If they are not independent, it may.  

For example, one possible model is:
For each bucket, and each letter A to Z, with some given probability p
you put that letter in the bucket.  However, with probability (1-p)^26
this will leave 0 letters in the bucket.  In that case you start again.
The result is that each bucket contains a given letter with probability
p/(1 - (1-p)^26).

Another possible model:
For bucket #1, do as in the previous example.  Then, given bucket #i,
for bucket #(i+1) take a copy of bucket #i, remove one letter at random
and, if bucket #i had fewer than 13 letters, replace it with two letters
randomly chosen from those that are not in bucket #i.  
--
Robert Israel              isr...@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

Thanks for your reply, Professor.

Where I said "each letter may appear only once," I should have been
more clear and said "each letter may appear only once per bucket."

Also, let's indeed assume a uniform distribution--for our purposes
here,
"Z" is as likely as "E." So, among the 5000 buckets, each bucket
could
have A through Z, or anything in-between. In other words, letters go
into the buckets randomly.

The buckets are indeed independent of each other, so, from what you've
said,
the number of buckets is irrelevant.

OTOH, only 2500 buckets have an A. And 2500 buckets have a B.
But not likely the same buckets, only 1250 will have AB. And only
625 will have ABC, only 312 will have ABCD, etc.

Will any of the 5000 have ABCDEFGHIJKLMNOPQRSTUVWXYZ?



-- Jeff

On Wed, 29 Jul 2009 11:54:58 -0700, jefftyzzer wrote:

(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

Thanks,

--Jeff

It depends on how the letters got put in the buckets. If, for example,
the letters were taken from a page in a book, then it's much more likely
that an E shows up than an X.

On Jul 29, 4:15 pm, Mensanator <mensana...@aol.com> wrote:





On Jul 29, 6:00 pm, jefftyzzer <jefftyz...@sbcglobal.net> wrote:

On Jul 29, 2:57 pm, Robert Israel

isr...@math.MyUniversitysInitials.ca> wrote:
(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

You didn't give us enough information.  How do you decide which letters
go into which buckets?  

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

If the contents of the buckets are independent, the 5000 doesn't matter.
If they are not independent, it may.  

For example, one possible model is:
For each bucket, and each letter A to Z, with some given probability p
you put that letter in the bucket.  However, with probability (1-p)^26
this will leave 0 letters in the bucket.  In that case you start again.
The result is that each bucket contains a given letter with probability
p/(1 - (1-p)^26).

Another possible model:
For bucket #1, do as in the previous example.  Then, given bucket #i,
for bucket #(i+1) take a copy of bucket #i, remove one letter at random
and, if bucket #i had fewer than 13 letters, replace it with two letters
randomly chosen from those that are not in bucket #i.  
--
Robert Israel              isr...@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

Thanks for your reply, Professor.

Where I said "each letter may appear only once," I should have been
more clear and said "each letter may appear only once per bucket."

Also, let's indeed assume a uniform distribution--for our purposes
here,
"Z" is as likely as "E." So, among the 5000 buckets, each bucket
could
have A through Z, or anything in-between. In other words, letters go
into the buckets randomly.

The buckets are indeed independent of each other, so, from what you've
said,
the number of buckets is irrelevant.

OTOH, only 2500 buckets have an A. And 2500 buckets have a B.
But not likely the same buckets, only 1250 will have AB. And only
625 will have ABC, only 312 will have ABCD, etc.

Will any of the 5000 have ABCDEFGHIJKLMNOPQRSTUVWXYZ?

-- Jeff

Realistically, no--no bucket will have all 26 letters.

But to keep it
simple, let's say it's *possible*.

On Jul 29, 7:25 pm, jefftyzzer <jefftyz...@sbcglobal.net> wrote:



On Jul 29, 4:15 pm, Mensanator <mensana...@aol.com> wrote:

On Jul 29, 6:00 pm, jefftyzzer <jefftyz...@sbcglobal.net> wrote:

On Jul 29, 2:57 pm, Robert Israel

isr...@math.MyUniversitysInitials.ca> wrote:
(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

You didn't give us enough information.  How do you decide which letters
go into which buckets?  

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

If the contents of the buckets are independent, the 5000 doesn't matter.
If they are not independent, it may.  

For example, one possible model is:
For each bucket, and each letter A to Z, with some given probability p
you put that letter in the bucket.  However, with probability (1-p)^26
this will leave 0 letters in the bucket.  In that case you start again.
The result is that each bucket contains a given letter with probability
p/(1 - (1-p)^26).

Another possible model:
For bucket #1, do as in the previous example.  Then, given bucket #i,
for bucket #(i+1) take a copy of bucket #i, remove one letter at random
and, if bucket #i had fewer than 13 letters, replace it with two letters
randomly chosen from those that are not in bucket #i.  
--
Robert Israel              isr...@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

Thanks for your reply, Professor.

Where I said "each letter may appear only once," I should have been
more clear and said "each letter may appear only once per bucket."

Also, let's indeed assume a uniform distribution--for our purposes
here,
"Z" is as likely as "E." So, among the 5000 buckets, each bucket
could
have A through Z, or anything in-between. In other words, letters go
into the buckets randomly.

The buckets are indeed independent of each other, so, from what you've
said,
the number of buckets is irrelevant.

OTOH, only 2500 buckets have an A. And 2500 buckets have a B.
But not likely the same buckets, only 1250 will have AB. And only
625 will have ABC, only 312 will have ABCD, etc.

Will any of the 5000 have ABCDEFGHIJKLMNOPQRSTUVWXYZ?

-- Jeff

Realistically, no--no bucket will have all 26 letters.

That's where the number of buckets matters. The more buckets you have,
the more likely some bucket will have all 26 letters.

But to keep it
simple, let's say it's *possible*.

Sure, even with a single bucket, it's always possible.
Although you wouldn't want to bet 5000, there is some
number of buckets that you would bet on.

On Jul 29, 6:19 pm, Mensanator <mensana...@aol.com> wrote:



On Jul 29, 7:25 pm, jefftyzzer <jefftyz...@sbcglobal.net> wrote:

On Jul 29, 4:15 pm, Mensanator <mensana...@aol.com> wrote:

On Jul 29, 6:00 pm, jefftyzzer <jefftyz...@sbcglobal.net> wrote:

On Jul 29, 2:57 pm, Robert Israel

isr...@math.MyUniversitysInitials.ca> wrote:
(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

You didn't give us enough information.  How do you decide which letters
go into which buckets?  

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

If the contents of the buckets are independent, the 5000 doesn't matter.
If they are not independent, it may.  

For example, one possible model is:
For each bucket, and each letter A to Z, with some given probability p
you put that letter in the bucket.  However, with probability (1-p)^26
this will leave 0 letters in the bucket.  In that case you start again.
The result is that each bucket contains a given letter with probability
p/(1 - (1-p)^26).

Another possible model:
For bucket #1, do as in the previous example.  Then, given bucket #i,
for bucket #(i+1) take a copy of bucket #i, remove one letter at random
and, if bucket #i had fewer than 13 letters, replace it with two letters
randomly chosen from those that are not in bucket #i.  
--
Robert Israel              isr...@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

Thanks for your reply, Professor.

Where I said "each letter may appear only once," I should have been
more clear and said "each letter may appear only once per bucket."

Also, let's indeed assume a uniform distribution--for our purposes
here,
"Z" is as likely as "E." So, among the 5000 buckets, each bucket
could
have A through Z, or anything in-between. In other words, letters go
into the buckets randomly.

The buckets are indeed independent of each other, so, from what you've
said,
the number of buckets is irrelevant.

OTOH, only 2500 buckets have an A. And 2500 buckets have a B.
But not likely the same buckets, only 1250 will have AB. And only
625 will have ABC, only 312 will have ABCD, etc.

Will any of the 5000 have ABCDEFGHIJKLMNOPQRSTUVWXYZ?

-- Jeff

Realistically, no--no bucket will have all 26 letters.

That's where the number of buckets matters. The more buckets you have,
the more likely some bucket will have all 26 letters.

But to keep it
simple, let's say it's *possible*.

Sure, even with a single bucket, it's always possible.
Although you wouldn't want to bet 5000, there is some
number of buckets that you would bet on.

Maybe another formulation of the problem will help (your patience is
appreciated--probability is obviously not my core competency):

50 shoppers are in a supermarket that has an unlimited supply of
exactly 10 (different) products. All products are equally popular/
necessary, i.e., each product is as likely to be interesting to one
shopper as the next. What's the equation that expresses the
probability that if I check person X's basket, I'll find product Y?

--Jeff

(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

On Jul 29, 2:57 pm, Robert Israel



isr...@math.MyUniversitysInitials.ca> wrote:
(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

You didn't give us enough information.  How do you decide which letters
go into which buckets?  

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

If the contents of the buckets are independent, the 5000 doesn't matter..
If they are not independent, it may.  

For example, one possible model is:
For each bucket, and each letter A to Z, with some given probability p
you put that letter in the bucket.  However, with probability (1-p)^26
this will leave 0 letters in the bucket.  In that case you start again.
The result is that each bucket contains a given letter with probability
p/(1 - (1-p)^26).

Another possible model:
For bucket #1, do as in the previous example.  Then, given bucket #i,
for bucket #(i+1) take a copy of bucket #i, remove one letter at random
and, if bucket #i had fewer than 13 letters, replace it with two letters
randomly chosen from those that are not in bucket #i.  
--
Robert Israel              isr...@math.MyUniversitysInitials.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

Thanks for your reply, Professor.

Where I said "each letter may appear only once," I should have been
more clear and said "each letter may appear only once per bucket."

Also, let's indeed assume a uniform distribution--for our purposes
here,
"Z" is as likely as "E." So, among the 5000 buckets, each bucket
could
have A through Z, or anything in-between. In other words, letters go
into the buckets randomly.

The buckets are indeed independent of each other, so, from what you've
said,
the number of buckets is irrelevant.

-- Jeff

(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

Thanks,

--Jeff

On Jul 29, 6:19�pm, Mensanator <mensana...@aol.com> wrote:





On Jul 29, 7:25�pm, jefftyzzer <jefftyz...@sbcglobal.net> wrote:

On Jul 29, 4:15�pm, Mensanator <mensana...@aol.com> wrote:

On Jul 29, 6:00�pm, jefftyzzer <jefftyz...@sbcglobal.net> wrote:

On Jul 29, 2:57�pm, Robert Israel

isr...@math.MyUniversitysInitials.ca> wrote:
(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a homework problem (I only
wish it were). While this is definitely work-related, I've made it
generic by analogizing the problem by referring to buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each bucket can contain
between 1 and 26 of the letters A-Z (but each letter only once), what
is the probability that any given letter will be in a given bucket?

You didn't give us enough information. �How do you decide which letters
go into which buckets? �

It seems like the answer is simply 1/26, but I'm wondering if the fact
that I have a known quantity of buckets changes things, likewise for
the prohibition that each letter may appear only once. In other words,
are there some nuances I'm ignorant of that make this problem more
challenging that it first appears to be?

If the contents of the buckets are independent, the 5000 doesn't matter.
If they are not independent, it may. �

For example, one possible model is:
For each bucket, and each letter A to Z, with some given probability p
you put that letter in the bucket. �However, with probability (1-p)^26
this will leave 0 letters in the bucket. �In that case you start again.
The result is that each bucket contains a given letter with probability
p/(1 - (1-p)^26).

Another possible model:
For bucket #1, do as in the previous example. �Then, given bucket #i,
for bucket #(i+1) take a copy of bucket #i, remove one letter at random
and, if bucket #i had fewer than 13 letters, replace it with two letters
randomly chosen from those that are not in bucket #i. �
--
Robert Israel � � � � � � �isr...@math.MyUniversitysInitials.ca
Department of Mathematics � � � �http://www.math.ubc.ca/~israel
University of British Columbia � � � � � �Vancouver, BC, Canada

Thanks for your reply, Professor.

Where I said "each letter may appear only once," I should have been
more clear and said "each letter may appear only once per bucket."

Also, let's indeed assume a uniform distribution--for our purposes
here,
"Z" is as likely as "E." So, among the 5000 buckets, each bucket
could
have A through Z, or anything in-between. In other words, letters go
into the buckets randomly.

The buckets are indeed independent of each other, so, from what you've
said,
the number of buckets is irrelevant.

OTOH, only 2500 buckets have an A. And 2500 buckets have a B.
But not likely the same buckets, only 1250 will have AB. And only
625 will have ABC, only 312 will have ABCD, etc.

Will any of the 5000 have ABCDEFGHIJKLMNOPQRSTUVWXYZ?

-- Jeff

Realistically, no--no bucket will have all 26 letters.

That's where the number of buckets matters. The more buckets you have,
the more likely some bucket will have all 26 letters.

But to keep it
simple, let's say it's *possible*.

Sure, even with a single bucket, it's always possible.
Although you wouldn't want to bet 5000, there is some
number of buckets that you would bet on.

Maybe another formulation of the problem will help (your patience is
appreciated--probability is obviously not my core competency):

50 shoppers are in a supermarket that has an unlimited supply of
exactly 10 (different) products. All products are equally popular/
necessary, i.e., each product is as likely to be interesting to one
shopper as the next. What's the equation that expresses the
probability that if I check person X's basket, I'll find product Y?

--Jeff

(Note: cross-posted in alt.sci.math.probability)

Friends,

First, I want to assure you that this isn't a
homework problem (I only
wish it were). While this is definitely work-related,
I've made it
generic by analogizing the problem by referring to
buckets and letters
(I don't do much work with buckets .

Question: If I have, say, 5,000 buckets, and each
bucket can contain
between 1 and 26 of the letters A-Z (but each letter
only once), what
is the probability that any given letter will be in a
given bucket?

It seems like the answer is simply 1/26, but I'm
wondering if the fact
that I have a known quantity of buckets changes
things, likewise for
the prohibition that each letter may appear only
once. In other words,
are there some nuances I'm ignorant of that make this
problem more
challenging that it first appears to be?

Thanks,

--Jeff

Question: If I have, say, 5,000 buckets, and each
bucket can contain between 1 and 26 of the letters
A-Z (but each letter only once), what is the
probability that any given letter will be in a
given bucket?