Three actors and two dancers have individual auditions for a musical

Question

Three actors and two dancers have individual auditions for a musical during the same afternoon. If no two actors are allowed to audition immediately following each other, in how many different orders could the five performers be seen?

A. 3
B. 6
C. 12
D. 24
E. 120

Show Answer

Official Answer

C

A. 3
B. 6
C. 12
D. 24
E. 120

sj296 · Answer

Let's say actors are A1 A2 & A3

Dancers are D1 & D2

Possible order of the performance = D1 A1 D2 A2 A3 or A1 D1 A2 D2 A3

It is clear that dancers can not be in the beginning or at the ending. They have to be in between

Actor Dancer Actor Dancer Actor should be the order

=> first place can be filled in 3 ways (3C1)
=> second place can be filled in 2 ways (2C1)
=> third place can be filled in 2 ways (2C1)
=> fourth & fifth place can be filled on 1 - 1 way

So total number of orders = 3*2*2*1*1 = 12

IMO OA should be C

charkia · Answer

Let's assume A stands for actor and D stands for dancer. According to the question stem, the order of performance can only be A D A D A because no two actors can audition after each other.

Number of ways the actors can be arranged = 3! = 6

Number of ways the dancers can be arranged = 2! = 2

6 x 2 = 12

so the OA is (C) imo

luisdicampo · Answer

Deconstructing the Question  
There are  5 distinct performers : 3 actors and 2 dancers.
Constraint:  no two actors can be consecutive .
So the 3 actors must be separated by the dancers.

Step-by-step  
Arrange the 2 dancers first:
 2! = 2  ways.

With the dancers placed, we have 3 slots around them:
 \_ \ D \ \_ \ D \ \_

To avoid consecutive actors, each slot can contain  at most one  actor.
We have 3 actors and 3 slots, so all 3 slots must be filled.

Arrange the 3 actors in those 3 slots:
 3! = 6  ways.

Total valid orders:
 2! \cdot 3! = 2 \cdot 6 = 12

Answer:     (C) 12

Three actors and two dancers have individual auditions for a musical

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Three actors and two dancers have individual auditions for a musical

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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