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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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