Question

A committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is

• A. $2720$
• B. $2702$
• C. $2270$
• D. $2278$

Answer 1

The correct option is B $2702$

As the number of women are need to be greater and the total number of members should be 12 therefore the permutations are

let women be W and men be M

(9W,3M),(8W,4M),(7W,5M)

${}^9{C}_9{\times }^8{C}_3{+}^9{C}_8{\times }^8{C}_4{+}^9{C}_7{\times }^8{C}_5$

$1\times 56+9\times 70+36\times 56=2702$