Help Show All Work 18 1921 18 A studio needs 3 actors for th

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18.

19-21

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 stadio select? a) b) (more)

Solution

18.   6 actors available are Moe, Larry, Curly, Shemp, Joe, and Curly Joe.

a) combinations of 3 actors = 6C3 = 6!/(3!3!) = 6*5*4/6 = 20 ways

b) Moe must be one of the actors. Remaining 5 actors and we have to choose 2 actors

possible combination = 5C2 = 5!/(2!3!) = (5*4)/2 = 10

c) Moe must be one of the actors, but also, that Shemp refuses to work with either Joe or Curly Joe.

Actors : Moe, Larry, Curly, Shemp, Joe, and Curly Joe

Possible combinations: Moe + Shemp +Larry ;Moe + Shemp +Curly

Moe + Larry +Joe ;  Moe + Larry + C urlyJoe

Moe +Larry +curly ; Moe + curly+joe ; Moe + curly +curly joe

Possible combinations =7