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Oxford Entrance Exam Problem 4

Probability Level 3

$\large (1+xy+y^2)^n$

Let $n$ be a positive integer. The coefficient of $x^3y^5$ in the expansion of the expression above equals to?

\binom{n}{8}

n

\binom{n}{3}\binom{n}{5}

2^n

4\binom{n}{4}

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by Andrei Golovanov

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