If \(\frac{n!}{(n-3)!}=210\) then what is the value of (n)?

Correct answer: 7

Since \(n!=n(n-1)(n-2)(n-3)!\), we get \(\frac{n!}{(n-3)!}=n(n-1)(n-2)\). Thus, \(n(n-1)(n-2)=210\). As \(7\times6\times5=210\), the value of \(n\) is 7. For the closest distractor, \(n=6\) gives \(6\times5\times4=120\), not 210. Exam tip: In a factorial ratio, expand the larger factorial only up to the smaller factorial and cancel common factors.