Respuesta :
Answer:
If she wants at least one comedy, there are 1484 different combinations.
Step-by-step explanation:
The order in which she wants to pick the movies is not important. So, we use the combinations formula to solve this question.
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]
In this question:
She wants combinations of 3 movies, with at least one comedy. The easiest way to find this is finding the total number of combinations of 3 movies, from the set of 25(18 children's and 7 comedies), and subtract by the total number without comedies(which is 3 from a set of 25). So
Total:
3 from a set of 25.
[tex]C_{25,3} = \frac{25!}{3!(25-3)!} = 2300[/tex]
Without comedies:
3 from a set of 18.
[tex]C_{18,3} = \frac{18!}{3!(18-3)!} = 816[/tex]
At least one comedy:
[tex]2300 - 816 = 1484[/tex]
If she wants at least one comedy, there are 1484 different combinations.
