University of South Carolina High School Math Contest/1993 Exam/Problem 8
What is the coefficient of in the expansion of
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 .