Permutation-Combination
Aptitude

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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

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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   $\text{Men}$

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

$={^5C_3} ×{^6C_1}$

$= \textbf{60}$


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