Question

A student has to answer any $6$ questions out of $10$ questions came in the question paper. How many number of combinations of question are possible?

• A. $\frac{10!}{6!}$
• B. $\frac{10!}{4!}$
• C. $\frac{10!}{4!6!}$
• D. $\frac{10!}{6!6!}$

Answer 1

The correct option is C $\frac{10!}{4!6!}$

There are $10$ questions in question paper out which student have to give answers of any $6$ questions.

We have to find total number of combinations possible for selecting those questions.

This can be done in ${}^{10}{C}_6$ number of ways.

$\Rightarrow {}^{10}{C}_6=\frac{10!}{(10-6)!6!}=\frac{10!}{4!.6!}$