Question

Howard is picking out some movies to rent, and he has narrowed down his selections to 4 children's movies, 7 comedies, 7 mysteries, and 5 horror films. How many different combinations of 9 movies can he rent if he wants all 4 children's movies

Answer 1

6188

Explanation:

Number of children's movies = 4

Number of comedy movies = 7

Number of mystery movies = 7

Number of horror movies = 5

Total number of movies to be rented = 9 out of which 4 are fixed to be children's movies

To find:

Number of different combinations to rent 9 movies out of which 4 are children's movies

Solution:

Number of movies left to be rented = 9 - 4 = 5

Number of movies left out of which these 5 are to be rented = 7 + 7 + 5 = 17

Now, there are a total of 17 movies out of which 5 are to be selected.

Therefore, we can use:

`_nC_r = (n! )/(r!(n-r)!)`

where,
`n = 17`

`r = 5`

`_(17)C_5 = (17! )/(5!(12)!)\\\Rightarrow (17.16.15.14.13)/(5.4.3.2.1) = \bold{6188}`