Question

Roxie is picking out some movies to rent, and she is primarily interested in horror films and foreign films. She has narrowed down her selections to 20 horror films and 8 foreign films. Step 2 of 2 : How many different combinations of 3 movies can she rent if she wants at least two horror films

Answer 1

2470

Explanation:

Roxie must pick 3 movies from 20 horror films and 8 foreign films with at least two horror films.

i) She can pick 2 horror films and 1 foreign film

The number ways this is possible = C(20, 2) * C(8, 1)

`C(20,2)=(20!)/((20-2)!2!)=190\\\\C(7,1)=(7!)/((7-1)!1!)=7`

The number ways this is possible = C(20, 2) * C(8, 1) = 190 * 7 = 1330

ii) She can pick 3 horror films

The number ways this is possible = C(20, 3)

`C(20,3)=(20!)/((20-3)!3!)=1140\\\\`

The number ways this is possible = C(20, 3) = 1140

The number of ways of picking 3 movies from 20 horror films and 8 foreign films with at least two horror films = pick 2 horror films and 1 foreign film + pick 3 horror films

The number of ways of picking 3 movies from 20 horror films and 8 foreign films with at least two horror films = 1330 + 1140 =2470