Answer:
Explanation:
1. Assume that Juan picks one horror film and two mystery films.
The number of different combinations of one horror film is C(7,1), and the number of different combinations to pick two mystery films is C(13,2).
Thus, the total number of different combinations for this option is C(7,1) × C(13,2)
2. If Juan picks two horror films and one mystery film.
The number of different combinations of two horror films is C(7,2), and the number of different combinations of one mystery film is C(13,1).
Thus the total number of different combinations for this option is C(7,2) × C(13,1).
3. If Juan picks three horror films.
The number of different combinations of three horror films is C(7,3).
4. The total number of different combinations is the sum of all those combinations:
The formula for combinations is:
[tex]C(m,n)=\dfrac{m!}{n!(m-n)!}[/tex]
Then:
[tex]C(7,1)=\dfrac{7!}{1!.6!}=7[/tex]
[tex]C(13,2)=\dfrac{13!}{2!.11!}=78[/tex]
[tex]C(7,2)=\dfrac{7!}{2!.5!}=21[/tex]
[tex]C(13,1)=\dfrac{13!}{1!.12!}=13[/tex]
[tex]C(7,3)=\dfrac{7!}{3!.4!}=35[/tex]
[tex]7\times 78+21\times 13+35=546+273+35=854[/tex] ← answer
