University of South Carolina High School Math Contest/1993 Exam/Problem 8
From AoPSWiki
Problem
What is the coefficient of 
in the expansion of
Solution
If we expand out the given product, we see that we have a sum of terms in which each term is a product of six members of the set 
(with repetitions allowed). In order to have one of these terms equal to , we can either have a single term and five terms of 1 in our product (
ways) or one 
term, one 
term and four 1 terms (
ways) or have three terms (
ways). This gives us a total of 
.
