Algebra 2 help!!

Question

A studio needs 3 actors for their short comedy film. The 6 actors available are Moe, Larry, Curly, Shemp, Joe, and Curly Joe.
a) How many different combinations of 3 actors can the studio choose?
b) Suppose Moe must be one of the actors. How many different combinations of 3 actors can the studio now choose?
c) Suppose Moe must be one of the actors, but also, that Shemp refuses to work with either Joe or Curly Joe. Now how many different combinations of 3 actors can the studio select?

Answer 1

a.  there are 6C3 different possible ways to select 3 actors from the list of six possible actors. this number is 20.

b. 5C2 ways to choose, if Moe is pre-selected. this is 10.

c.  Moe is pre-selected. if Shemp is chosen, then there are exactly 2 acceptable choices for the third person.

if Shemp is NOT chosen, then there are 4C2, or six, possible choices for the other two.

the answer in this case is therefore 2+6 = 8.

 

Check this out for yourself; do you agree?