For integers \(n>r\geq 0\), which expression correctly represents \((r+1)(r+2)\cdots n\) in factorial notation?

Correct answer: \(\frac{n!}{r!}\)

Since \(n!=1\cdot2\cdots r\cdot(r+1)(r+2)\cdots n\) and \(r!=1\cdot2\cdots r\), dividing \(n!\) by \(r!\) cancels the initial factors. Hence \((r+1)(r+2)\cdots n=\frac{n!}{r!}\). \((n-r)!\) is the factorial of the number of terms, not the product of the given terms. Exam tip: cancel the common initial factors in a factorial fraction to verify the result.