Question

Suppose that 9 female and 6 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 15 ?finalists, what is the probability of selecting no? females?

Answer 1

Answer:
`(2)/(1001)`

Explanation:

Given : The number of female applicants = 9

The number of male applicants = 6

Total applicants = 15

The number of ways to select 5 applicants from 15 applicants :-

`^(15)C_5=(15!)/(5!(15-5)!)=3003`

The number to select 5 applicants from 15 applicants such that no female applicant is selected:-

`^(9)C_0*^6C_5=1*(6!)/(5!(6-5)!)=6`

Now, the required probability :-

`(6)/(3003)=(2)/(1001)`