Question

A committee of 7 has to be formed 9 boys and 4 girls in how many ways can this be done when the committee consist of atleast 3 girls ?

Answer 1

Number of girls $=4$
Number of boys $=9$
Since the committee has to consist at least $3$ girls, the committee can consists of
(a) $3$ girls and $4$ boys
(b) $4$ girls and $3$ boys
(a) $3$ girls and $4$ boys can be selected in ${=}^4{C}_3{\times }^9{C}_4$ ways
(b) $4$ girls and $3$ boys can be selected in ${=}^4{C}_4{\times }^9{C}_3$ ways
$\therefore$ Required number of ways
${=}^4{C}_3{\times }^9{C}_4{+}^4{C}_4{\times }^9{C}_3$
$=4\times 126+1\times 84=504+84=588$