University of South Carolina High School Math Contest/1993 Exam/Problem 8
Problem
What is the coefficient of in the expansion of
![$4 (1 + x + x^2 + x^3 + x^4 + x^5 )^6?$](http://latex.artofproblemsolving.com/9/5/0/950100c82ab65682e2e0bfd82ac80f7b3ef638f5.png)
![$\mathrm{(A) \ } 40 \qquad \mathrm{(B) \ }48 \qquad \mathrm{(C) \ }56 \qquad \mathrm{(D) \ }62 \qquad \mathrm{(E) \ } 64$](http://latex.artofproblemsolving.com/d/3/7/d37b89c36eabc473792f9ed081d97757a8f69f3d.png)
Solution
The expression simplifies to . Expanding both the numerator and denominator, we see that the coefficient of the
term is
.