Mathematics: 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

its cStep-by-step explanation:...

Howard is picking out some movies to rent, and

crystalclear99

16.03.2022

6188

Step-by-step 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:

$_nC_r = \dfrac{n! }{r!(n-r)!}$

where, n = 17

r = 5

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

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