The director is looking at eight performers for the roles of Luke Skywalker, Han Solo and Darth Vader. How many ways are there that the director cast these three roles?

Question

1. In the school play of Star Wars, the director is looking at eight performers for the roles of Luke Skywalker, Han Solo and Darth Vader. 

How many ways are there that the director cast these three roles?

Answer 1

8 choose 3 = 8!/(5!*3!) = 8*7*6/(3*2) = 4*7*2 = 56.