Question

Antoine is picking out some movies to rent, and he has now the down his selection to 4 Mysteries, 3comedies, 3 horror films, and 6documentaries. How many different combinations of 9movies can he rent if he wants all 4 Mysteries?

Answer 1

Given:

Movies to rent:

4 = mysteries

3 = comedies

3 = horror

6 = documentaries

Asked: How many different combinations of 9 movies can he rent if he wants all 4 Mysteries? ​

Solution:

The total choices Antoine has is 4+3+3+6 = 16 movies to rent.

Out of the 16 movies, he wants all 4 mystery movies so, we will subtract 4 to the total number of movies to rent.

We will have a new total number of movies to rent of 16 - 4 = 12

Antoine will rent 9 movies in total.

Out of 9 movies, 4 movies are mystery movies. 9 - 4 = 5

The combination of the remaining 5 slots out of 9 with the 12 other categories of movies would be:

`\begin{gathered} nCr\text{ = }(n!)/(r!(n-r)!) \\ 12C5\text{ = }(12!)/(5!(5-1)!) \\ 12C5\text{ = 792} \end{gathered}`

ANSWER: There are 792 different combinations Antoine can get.