Answer:
He can rent 1001 different combinations of 9 movies can he rent if he wants all 5 mysteries.
Step-by-step explanation:
The order is not important.
For example watching horror movie A and then horror movie B is the same combination as watching horror movie B then horror movie A. So we use the combinations formula to solve this problem.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many different combinations of 9 movies can he rent if he wants all 5 mysteries?
There are 4+5+6+4 = 19 total movies.
He wants to watch all five mysteries(combination of 5 from a set of 5) and 4 of the other 19-5 = 14 movies. So
[tex]T = C_{5,5}*C_{14,4} = \frac{5!}{5!(5-5)!}*\frac{14!}{4!(14-4)!} = 1001[/tex]
He can rent 1001 different combinations of 9 movies can he rent if he wants all 5 mysteries.
