Mock AIME 1 2007-2008 Problems/Problem 1

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Problem

What is the coefficient of $x^3y^{13}$ in $\left(\frac 12x + y\right)^{17}$?

Solution

In a binomial expansion, the sum of the degrees of the power of each of the two terms must sum to the power being raised to, here $17$. However, $3 + 13 = 16$, contradiction; so there does not exist such a term, and the answer is $\boxed{000}$.

See also

Mock AIME 1 2007-2008 (Problems, Source)
Preceded by
First question
Followed by
Problem 2
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