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 :-
[tex]^{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[/tex]
Hence, the number of different combinations of 4 movies can he rent if he wants at least two comedies = 31,365
