Question

From $7$ boys and $4$ girls a committee of $6$ is to be formed. The number of ways in which the selection can be done when the committee contains exactly two girls is:

• A. $210$
• B. $220$
• C. $371$
• D. $480$

Answer 1

Answer: (A)

$210$

Since committee contains exactly two girls so we have to select $4$ boys out of $7$ boys and two girls from $4$ girls.
Selection of $4$ boys from $7$ can be done in ${}^7{C}_4$ ways
And selection of two girls from $4$ can be done in ${}^4{C}_2$ ways
Thus using multiplication principle,
Required number of ways $={}^7{C}_4\times {}^4{C}_2=35\times 6=210$