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### Collecting a Complete Set

```
Date: 03/15/2000 at 07:18:55
From: Keith Butler
Subject: Probability/Combinations

I have a very large box filled with 8 different frying pan handles in
equal proportions. What is the probability that I will have to remove
32 handles before I get a complete set?

I'm thinking combinations but the formulas I find don't seem to apply,
and when I work it through it my head, even with a smaller number of
handles, my brain blows up by the potential number of combinations.

Thank you very much,
Keith
```

```
Date: 03/15/2000 at 12:07:54
From: Doctor Anthony
Subject: Re: Probability/Combinations

The number of possible results is 8^32 (i.e. there are 8 possible
results each time a handle is chosen.)

A simple model will be that of throwing an 8-sided die 32 times (n =
32) and finding the probabilities of N = 1, 2, 3, 4, 5, 6, 7, 8
different numbers.

This can further be modeled by thinking of distributing 32 balls into
N = 1, 2, 3, 4, 5, 6, 7, 8 urns.

To deal with equi-probable outcomes we must use the T(n,m) function.
For an explanation of the T(n,m) function, see:

Collecting a Set of Coupons
http://mathforum.org/dr.math/problems/amal2.2.3.00.html

- Doctor Anthony, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Permutations and Combinations
High School Probability

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