If \( \frac{(n+1)!}{(n-3)!}=5040 \), what is the value of (n)?

Correct answer: 9

Cancelling \((n-3)!\) from \((n+1)!\) gives \(\frac{(n+1)!}{(n-3)!}=(n+1)n(n-1)(n-2)\). Hence, \((n+1)n(n-1)(n-2)=5040\). For \(n=9\), \(10\times9\times8\times7=5040\), so the correct value is \(9\). For \(n=8\), the product is \(9\times8\times7\times6=3024\), not 5040. Exam tip: In factorial ratios, expand the larger factorial only up to the smaller factorial and then cancel common terms.