Question

A committee of $5$ members is to be formed from $6$ boys and $5$ girls. The number of ways in which the committee can be formed so that the committee must contain at least one boy and one girl having majority of boys is

• A. $240$
• B. $245$
• C. $250$
• D. $275$

Answer 1

The correct option is D $275$

Required committee should contain $3$ boys, $2$ girls or $4$ boys, $1$ girl
$\therefore$ Number of ways for committee to be formed
$={}^6{C}_3\times {}^5{C}_2+{}^6{C}_4\times {}^5{C}_1=275$