Aptitude 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:

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

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

$= \textbf{4914}$