Answer:
2470
Step-by-step 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)
[tex]C(20,2)=\frac{20!}{(20-2)!2!}=190\\\\C(7,1)=\frac{7!}{(7-1)!1!}=7[/tex]
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)
[tex]C(20,3)=\frac{20!}{(20-3)!3!}=1140\\\\[/tex]
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
