is picking out some movies to rent, and he has narrowed down his selections to 5 documentaries, 7 comedies, 4 mysteries, and 5 horror films.

Question

is picking out some movies to rent, and he has narrowed down his selections to 5 documentaries, 7 comedies, 4 mysteries, and 5 horror films. How many different combinations of 9 movies can he rent if he wants all 7 comedies?

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Melody 2 weeks 2021-09-13T15:08:49+00:00 1 Answer 0

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    2021-09-13T15:10:06+00:00

    Answer: 91

    Step-by-step explanation:

    Given : The number of documentaries = 5

    The number of comedies = 7

    The number of mysteries = 4

    The number of horror films =5

    The total number of movies other than comedy = 14

    Now, the number of possible combinations of 9 movies can he rent if he wants all 7 comedies is given by :-

    ^7C_7\times^{14}C_2\\\\\dfrac{7!}{7!(7-7)!}\times\dfrac{14!}{2!(14-2)!}\\\\=(1)\times\dfrac{14\times13}{2}\\\\=91

    Therefore, the number of possible combinations of 9 movies can he rent if he wants all 7 comedies is 91 .

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