Question 31 pts8 men and 6 women apply for a job at a new startup. How manyways can 4 of the applicants be selected for a second interview?

Accepted Solution

Answer:1001 waysStep-by-step explanation:Total number of people who applied for the job = 8 + 6 = 14Number of people to be chosen = 4This is a combination problem because the order of selection does not matter. A group selection involves the combinations. So here we have to find the combinations of 14 people taken 4 at a time. The formula for the combination is:[tex]^{n}C_{r} = \frac{n!}{r!(n-r)!}[/tex]Here, n is the total number of objects which is 14 in this case.r is the number of objects to be chosen which is 4 in this case. Using these values, we get:[tex]^{14}C_{4}=\frac{14!}{4!(14-4)!}\\\\ = \frac{14!}{4! \times 10!}\\\\ =1001[/tex]Thus, there are 1001 ways to select 4 applicants from 8 men and 6 women for the second interview.