Aptitude Discussion

Q. |
There are five women and six men in a group. From this group a committee of $4$ is to be chosen. How many different ways can a committee be formed that contain three women and one man? |

✖ A. |
55 |

✔ B. |
60 |

✖ C. |
25 |

✖ D. |
192 |

**Solution:**

Option(**B**) is correct

Since no order to the committee is mentioned, a combination instead of a permutation is used.

Let’s sort out what we have and what we want.

Have: $5$ women, $6$ men.

Want: $3$ women AND $1$ man.

The word **AND** means multiply.

$\text{Woman}$ and $\text{Men}$

${^{ \text{have} }C_{\text{want}}} \;\; × \;\;{^{ \text{have} }C_{\text{want}}}$

$={^5C_3} ×{^6C_1}$

$= \textbf{60}$