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

A studio needs 3 actors for their short comedy film. The 6 actors available are Moe, Larry, Curly, Shemp, Joe, and Curly Joe, How many different combinations of 3 actors. How many different combinations of 3 actors can the studio now choose? 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?

Solution

a).

given that there are 6 actors available .

And studio needs 3 actors

the different number of combinations is =6C3 [ by using nCr formula of permutation and combination ]

= 6*5*4 / 3*2*1

= 5*4

= 20

b). given that moe must be in the studio

let us say _ _ _ be the actors ( _ is actor)

now fix one position for moe

now we have two more actors to be selected out of 5

the number ways of doing this is = 5C2

=5*4 /2

=20/2

=10

c) . now moe is must be in the studio

and shemp refused to work with joe or curly joe

the possible ways of doing this

moe , shemp , larry

moe , shemp,curly

moe,larry,curly

moe,joe, larry

totally 7 ways are possibe

moe ,joe,curly

moe,curly joe, curly

moe,curly joe, larry