Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Find a binomial coefficient in \((x+y)^n\) using combinations
Problem
Find the binomial coefficient of \(x^3y^2\) in \((x~+~y)^5\).
Big Picture
What this problem is really about
Use the target exponents to locate the term before calculating anything. In a power-n expansion, the exponent on the second variable is k and the exponent on the first is n minus k, so the pair must sum to n. Once k is identified and checked against both exponents, the coefficient is the corresponding combination.
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