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

Step-by-step 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 :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

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

$^{20}C_6=\dfrac{20!}{6!(20-6)!}\\\\=\dfrac{20\times29\times18\times17\times16\times15\times14!}{(720)14!}=38760$

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