Answer: 854
Step-by-step explanation:
Given , Number of horror films = 7
Number of mysteries = 13
Total movies = 13+7=20
Number of combinations of r things taken out of n things : [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Now , the number of combinations of 3 movies can he rent if he wants at least one horror film = [tex]^7C_1\times^{13}C_2+^7C_2\times^{13}C_1+^7C_3\times^{13}C_0[/tex]
[tex]=(7)\times\dfrac{13!}{2!(13-2)!}+\dfrac{7!}{2!(7-2)!}\times(13)+\dfrac{7!}{3!(7-3)!}(1)\\\\=546+273+35\\\\=854[/tex]
Hence, there are 854 different combinations of 3 movies can he rent if he wants at least one horror film .
