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 :-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Then, the number of different sets of employees could receive bonuses is given by :-
[tex]^{20}C_6=\dfrac{20!}{6!(20-6)!}\\\\=\dfrac{20\times29\times18\times17\times16\times15\times14!}{(720)14!}=38760[/tex]
Hence, the number of different sets of employees could receive bonuses is 38760.
