A university has hired 10 new employees and must assignee 6

A university has hired 10 new employees , and must assignee 6 employees to the day shift and 4 employees to the night shift

1) In how many ways can the assignment be made?

2)Assume that the 10 employees consists of 5 men and 5 women and that the assignments to the day and night are made at random. What is the probability that 4 of the night shift employees are men?

3)What is the probability that at least one of the night shift is a women?

Solution

1) NO of ways = 10C6

2) Prob (4 of the night shift employees are men) = 5C4/10C4

3) Prob ( atleast one woman in night shift) = 1- no woman in night shift

= 1- 5C4/10C4