Question

a company owner has 20 employees, and plans to give bonuses to 6 of them. How many different sets of employees could receive bonuses?

Answer 1

Answer: 38760

Explanation:

Given : The number of employees in the company = 20

The number of employees will be selected by company owner to give bonus = 6

We know that the combination of n things taking r at a time is given by :-

`^nC_r=(n!)/(r!(n-r)!)`

Then, the number of different sets of employees could receive bonuses is given by :-

`^(20)C_6=(20!)/(6!(20-6)!)\\\\=(20*29*18*17*16*15*14!)/((720)14!)=38760`

Hence, the number of different sets of employees could receive bonuses is 38760.