What is the value of \(\frac{10!}{7!,3!}\)?

Correct answer: 120

Write \(10! = 10\times 9\times 8\times 7!\), so \(7!\) cancels out. Thus, \(\frac{10!}{7!\,3!}=\frac{10\times9\times8}{3\times2\times1}=\frac{720}{6}=120\). Therefore, 120 is correct. The value 720 is only \(10\times9\times8\); division by \(3!\) is still required. Exam tip: In factorial fractions, expand the larger factorial only up to the smaller factorial and cancel first.