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/