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### Phone Number Combinations

```
Date: 05/07/2000 at 13:54:09
From: Sonja Moussa
Subject: Probability

Linda knows the first 3 digits of Jack's phone number, which are 297,
but she doesn't know the other 4. All she remembers is that the rest
of the digits are 2's, 9's and 7's. What is the maximum number of
times that Linda (who is very unlucky) will have to try until she gets
the right number?
```

```
Date: 05/08/2000 at 15:10:03
From: Doctor Anthony
Subject: Re: Probability

You can model this as the number of different ways you could put 4
balls at random into 3 cells (numbered 2, 9 and 7) such that no cell
is empty. The answer is 36 in this case. It is the value T(4,3). For
an explanation of the function T(n,m), see:

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

There, I have also given a general description of the method that
allows you to calculate far more difficult problems.

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

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