Combinations Examples on Men and Women

In this class, We discuss Combinations Examples on Men and Women.

The reader should have prior knowledge of combinations formulae. Click here.

Example:

A department consists of eight men and nine women. How many ways can we form a committee?

1) Three men and four women

8c3 ways to select men

9c4 ways to select women.

Total = 8c3 * 9c4

2) Committee of four with at least one woman.

Different possibilities to select from are given below

Three men and one woman.

Two men and two women.

One man and three women committee.

Total = 8c3 * 9c1 + 8c2 * 9c2 + 8c1 * 9c3

Total = 2310

3) Committee of four with at most one man.

Zero men and four women

one man and three women

Total = 8c0 * 9c4 + 8c1 * 9c3

Total = 798

4) A committee of four with two specific persons is not included.

The total selections of the four-member committee is 17c4

The total selection of two specific persons included in the four-member committee is 15c2.

Two specific persons not included = Total selections – Two specific included

= 17c4 – 15c2