The value of \(\frac{13!}{11!}\) is equal to which of the following?

Correct answer: \(13\cdot12\)

Factorials are products of consecutive positive integers. When one factorial is divided by a smaller factorial, expand the larger factorial only until the denominator’s factorial appears. This exposes the common factor and makes cancellation straightforward, avoiding unnecessary calculation of the very large values of 13! and 11!.

We write \(13!=13\times12\times11!\). Hence \(\frac{13!}{11!}=\frac{13\times12\times11!}{11!}=13\times12\). The common factor \(11!\) cancels, leaving the product shown in option B. Option C uses 11 instead of the factor immediately above the denominator, while the other choices do not represent the correct factorial expansion.