If \( \frac{(n+4)!}{n!}=11880 \), what will be the value of (n)?

Correct answer: 8

\(\frac{(n+4)!}{n!}=(n+4)(n+3)(n+2)(n+1)\). Thus, the product of four consecutive integers must be \(11880\). Since \(9\times10\times11\times12=11880\), we get \(n+1=9\), so \(n=8\). For instance, if \(n=7\), the product is \(8\times9\times10\times11=7920\), not \(11880\). Exam tip: cancel factorials first and rewrite the expression as a product of consecutive integers.