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: $\dfrac{2}{1001}$

Step-by-step 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 :-

$^{15}C_5=\dfrac{15!}{5!(15-5)!}=3003$

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

$^{9}C_0\times^6C_5=1\times\dfrac{6!}{5!(6-5)!}=6$

Now, the required probability :-

$\dfrac{6}{3003}=\dfrac{2}{1001}$