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:
[tex]\begin{gathered} nCr\text{ = }\frac{n!}{r!(n-r)!} \\ 12C5\text{ = }\frac{12!}{5!(5-1)!} \\ 12C5\text{ = 792} \end{gathered}[/tex]ANSWER: There are 792 different combinations Antoine can get.
