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?

Answer 1

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 .