Question

is picking out some movies to rent, primarily interested in horror films and comedies. He has narrowed down his selections to 15 horror films and 18 comedies. How many different combinations of 4 movies can he rent if he wants at least two comedies?

Answer 1

Answer: 31,365

Step-by-step explanation:

Given : The number of horror films = 15

The number of comedies = 18

Then , the number of different combinations of 4 movies can he rent if he wants at least two comedies is given by :-

$^{18}C_2\times ^{15}C_2+^{18}C_3\times ^{15}C_1+^{18}C_4\times ^{15}C_0\\\\=\dfrac{18!}{2!(18-2)!}\times\dfrac{15!}{2!(15-2)!}+\dfrac{18!}{3!(18-3)!}\times\dfrac{15!}{1!(15-1)!}+\dfrac{18!}{4!(18-4)!}\times\dfrac{15!}{0!(15-0)!}\\\\=16065+12240+3060=31365$

Hence, the  number of different combinations of 4 movies can he rent if he wants at least two comedies = 31,365