2005 iTest Problems/Problem 7

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Problem

Find the coefficient of the fourth term of the expansion of $(x+y)^{15}$.

Solution 1

The coefficient of the $n$th term in the expansion of $(x+y)^m$ is $\binom{m}{n}$. Plugging in $15$ for m and $4$ for n, we find that our answer is $\binom{15}{4}=\boxed{1365}$.