Question

A play has two roles for men and four roles for women. If five men and 12 women try out for these parts, in how many different ways can the director choose people for the roles?

Answer 1

Answer: 4950 ways

Explanation:

Given : Number of roles for men = 2

Number of roles for women = 4

We know that the combination of n things taken r at a time is given by :-

`^nC_r=(n!)/(r!(n-r)!)`

Then, If five men and 12 women try out for these parts then the number of different ways can the director choose people for the roles :-

`^5C_2* ^(12)C_4=(5!)/(2!(5-2)!)*(12!)/(4!(12-4)!)\\\\=10*495=4950`

Hence, the director can choose people for the roles in 4950 ways .