What is the value of ( \frac{6!}{3!}+\frac{5!}{2!} )?

Correct answer: (180)

Factorial notation means multiplying all positive integers down to 1. For example, \(6!=6\times5\times4\times3\times2\times1\). In a sum of fractions, calculate each fraction separately before adding the results. Cancelling factorial factors is often the quickest method.

The first term is \(\frac{6!}{3!}=\frac{720}{6}=120\). The second term is \(\frac{5!}{2!}=\frac{120}{2}=60\). Adding them gives \(120+60=180\). Therefore option D is correct. A common mistake is to add or cancel factorial symbols across the plus sign; cancellation can be done within each fraction, but the two separate terms must then be added normally.