18 A studio needs 3 actors for their short comedy film The 6

18. 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 may 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? a) b) c) (more) AMERICAN SCHOOL Lansing, IL A-(1083) 07/14-06

Solution

a) Total no. of actors = 06

We have to choose actors =03

Different possible combination of 3 actors = 6C3 = 6!/(3! 3!) = (6.5.4)/(3!) = 20

b) Now Moe is one of the actors , remaining actors =5

So, selection of remaining actors =2

Different possible combintaion of 2 actors = 5C2 = 5!/(2!)(3!) =10

c)Moe (M),Larry (L) ,Curly (C),Shemp(S) ,Joe(J) , Curly Joe(CJ)

Moe is one of the actors, Shrimp refuses to work with Joe or Curly Joe

Possible combination :(S,L) ( S,C) (L or C or J or CJ)

                             = 1 +1 +4C2 = 2 + 4!/(2!2!)

                        = 2 + 6 =8