What is the simplified value of \( \frac{14!}{10!\cdot4!}\div\frac{13!}{9!\cdot4!} \)?

Correct answer: \(\frac{7}{5}\)

Convert the division into multiplication by the reciprocal:
\(\frac{14!}{10!\cdot4!}\times\frac{9!\cdot4!}{13!}\). Cancelling \(4!\), and then using \(14!=14\cdot13!\) and \(10!=10\cdot9!\), gives \(\frac{14}{10}=\frac{7}{5}\). Hence, option B is correct. A value such as \(\frac{5}{4}\) can result from cancelling factorial terms in the wrong order. Exam tip: first change division into multiplication by the reciprocal, then cancel common factorial factors.