Item.

What is the coefficient of \(x^3y^2\) in the expansion of \((x+y)^5\text{?}\) We must choose 3 of the 5 copies of the binomial to contribute an \(x\text{.}\) There are \({5 \choose 3}\) ways to do this, so the coefficient is \({5 \choose 3}\text{.}\)