Question

A group consists of $4$ girls and $7$ boys.In how many ways can a team of $5$ members be selected if the team has no girl?

• A. $40$
• B. $25$
• C. $21$
• D. $30$

Answer 1

The correct option is C $21$

	Total Number	Number to be chosen	Number of ways to choose
Girls	$4$	$0$	${}^4{C}_0$
Boys	$7$	$5$	${}^7{C}_5$

$\begin{array}{c}Totalnumberofways{=}^4{C}_0{\times }^7{C}_5\\ =\frac{4!}{0!\left(4-0\right)!}\times \frac{7!}{5!\left(7-5\right)!}\\ =\frac{4!}{1\times \left(4\right)!}\times \frac{7!}{5!2!}\\ =1\times \frac{7\times 6\times 5!}{5!\times 2\times 1}\\ =\frac{7\times 6}{2}\\ =21\\ Hence,theoptionCistherequiredanswer.\end{array}$