Question

A company has hired 15 new employees, and must assign 6 to the day shift, 4 to the night shift, and 5 to the graveyard shift.
In how many ways can the assignment be made?

Answer 1

Answer:

630630

Step-by-step explanation:

Given:

Total number of new employee in the company (n) =  15

Number to be assign to day shift ($k_{1}$) = 6

Number to be assign to night shift ($k_{2}$) = 4

Number to be assign to graveyard shift ($k_{3}$) = 5

Solution:

Possible ways to assign day shift = $k_{1}!$ = 6!

Possible ways to assign night shift = $k_{2}!$ = 4!

Possible ways to assign graveyard shift = $k_{3}!$ = 5!

Possible ways to assign new employees = n! = 15!

Total number of ways assignment can be made = $\frac{n!}{k_{1}!k_{2}k_{3}!}=\frac{15!}{6!4!5!}$=630630