Question

B. A play contains 18 speaking roles, where 10 are male and 8 are female. If the director can choose from among 15 male actors to fill the male roles and 11 female actors to fill the female roles, how many different casts are possible?

Answer 1

3168

Explanation:

Here, we have s combination problem as we are selecting. The question is quite straightforward.

What the director needs to do is simply select 10 males from the total 15 males and also select 8 females from the total 11 females and add the results.

To select 10 from 15, we simply compute as 15C10 which equals 3003 ways

To select 8 from 11, we simply compute 11C8 which equals 165 ways

We simply add both to get the numbers of possible casts which is 3003 + 165 = 3168 possibilities