Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Connect a binomial coefficient to a concrete selection count
Problem
Interpret the coefficient of \(x^3y^2\) in \((x~+~y)^5\) as a selection count.
Big Picture
What this problem is really about
Think of the binomial power as repeated factors, with one selection made from each factor. A target exponent on the second term tells how many factor positions must contribute that term; all remaining positions contribute the first term. The coefficient counts the unordered sets of positions that satisfy this requirement, which is why a combination appears.
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