As a promotion, a video store decides to give away posters for recently released movies.

Question

1. As a promotion, a video store decides to give away posters for recently released movies.

a) If posters are available for 27 recent releases, in how many ways could the video-store owner choose 8 different posters for the promotion?

b) Are you able to calculate the number of ways mentally? Why or why not?

Please explain for each question.

Answer 1

There is a hint given in the problem statement when it says "how many ways could the video-store owner >>>choose<<< 8 different posters". It is telling you to use the formula for 27 choose 8.

n choose k = n! / k!(n-k)!

27 choose 8 = 27! / 8!(27-8)! = 27! / 8!(19)! = 2220075

As for part b), it seems unlikely that most people would be able to compute a large factorial like this one mentally.