Question

There are 10 teachers and 20 students out of which selection of $5$ students are made for a sports committee. Find the number of ways in which this selection can be done.

• A. $\frac{10!}{5!.5!}$
• B. $\frac{20!}{15!.5!}$
• C. $\frac{20!}{10!.5!}$
• D. None of the above

Answer 1

The correct option is B $\frac{20!}{15!.5!}$

There are $10$ teachers and $20$ students out of these $5$ students are selected for sports committee.

Here, selection of students is only done. No teachers are selected.

So, all the possible selection of $5$ students out of $20$ students are made and it is equal to ${}^{20}{C}_5.$

$\Rightarrow {}^{20}{C}_5=\frac{20!}{(20-5)!5!}=\frac{20!}{15!.5!}$