Originally Posted by

**MathIsNotFun** I like comedies, animations, and sci fi. A video stores has release wall has 7 sci fi, 2 westerns, 9 suspense, 3 foreign, 12 animation, 4 dramas and 10 comedies. **How many way can i choose 3 movies if**

a) There are no restrictions?

b) I must choose one of each type?

c) No more than two of the movies can be sci fi.

a) Total = 7+2+9+3+12+4+10 = 47 ... _{47}C_{3} = 16215 ways

b) _{12}C_{1} x _{10}C_{1} x _{7}C_{1} = 12 x 10 x 7 = 840 ways

c) _{7}C_{2} = 21 ... _{42}C_{3} + 21 = 11501 ways