Question

An employer will select 4 employees to organize a committee (a committee of size 4). There are 5 female and 6 male employees. Employer would like to select two male for this committee. In how many different ways can an employer organize the committee?

Answer 1

Solution:

Given:There are 5 female and 6 male employees.

A committee of size 4( that is: 4 employees) is to be selected to organize a committee.

Employer would like to select two male for this committee.

Thus committee of size 4 should consists of 2 male and 2 female employees.

Thus 2 male employees can be selected from 6 male in ₆C₂ ways and 2 female employees can be selected in 5 females in ₅C₂ ways.

The number of ways  an employer can organize the committee =  ₆C₂ X ₅C₂

Use following combination formula.

thus

The number of ways  an employer can organize the committee =  ₆C₂ X ₅C₂

The number of ways  an employer can organize the committee = 15 X 10

The number of ways  an employer can organize the committee = 150