Abraham is picking out some movies to rent, and he is primarily interested in mysteries and foreign films. He has narrowed down his selections to 9 mysteries and 8 foreign films. How many different combinations of 3 movies can he rent if he wants at least one foreign film?

596 possibilities

Step-by-step explanation:

If Abraham wants at least one of the three films to be foreign film, we have the following cases of composition of the 3 films he will pick:

- 1 foreign and 2 mystery

- 2 foreign and 1 mystery

- 3 foreign and 0 mystery

For the first option, the foreign film has 8 possibilities, and the mystery films will be a combination of 9 choose 2, which is 9*8/2 = 36 possibilities, so we have a total of 8*36 = 288 possibilities

For the second option, the mystery film has 9 possibilities, and the foreign films will be a combination of 8 choose 2, which is 8*7/2 = 28 possibilities, so we have a total of 9*28 = 252 possibilities

For the third option, we have a combination of 8 choose 3, which is 8*7*6/(3*2) = 56 possibilities.

So, in total, we have 288 + 252 + 56 = 596 possibilities.

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