Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. A committee is to be formed comprising $7$ members such that there is a simple majority of men and at least $1$ woman. The shortlist consists of $9$ men and $6$ women. In how many ways can this committee be formed?
 ✖ A. $3,724$ ✖ B. $3,630$ ✔ C. $4,914$ ✖ D. $3,824$

Solution:
Option(C) is correct

Three possibilities:

$1W+6M, 2W+5M, 3W+4M$

$⇒ ({^6C_1} × {^9C_6}) + ({^6C_2} × {^9C_5}) + ({^6C_3} × {^9C_4})$

$= \textbf{4914}$