Question

A committee of four is being formed randomly from the employees at a school: 5 administrators, 37 teachers, and 4 staff.How many ways can the committee be formed?

Answer 1

Let us sum all the members of the committee

`5+37+4=46`

Therefore, the number of ways committee of 4 can be formed from 46employees will be

`^(46)C_4`

The formula for combination is,

`C\left(n,r\right)=\lparen_r^n)^=(n!)/((r!(n-r)!))`

Given:

`n=46,r=4`

Therefore,

`C\left(n,r\right)=C\left(46,4\right)=(46!)/((4!(46-4)!))=(46!)/(4!×42!)=163185`

Hence, the answer is 163185ways.