A play needs three protagonists (a man, a woman, and a girl), two antagonists (a man and a
woman), and two supporting roles (a man and a boy). Six men, six women, three boys, and four
girls attended the auditions. The number of ways the roles can be cast is?
Answers
Given : A play need 3 P ( Man , Woman girl )
2 A ( Man Woman)
2 supporting ( Man Boy )
6 Men 6 Women 3 Boys 4 Girls Attended auditions
To Find : The number of ways the roles can be cast is:
Solution:
woman can be P or A
six women are there
2 women can be selected in ⁶C₂ = 15 ways and can be assigned role in 2! = 2 ways
Hence total ways role to woman can be assigned = 15 x 2 = 30
Man can be P ,A , supporting role
six men are there
3 men can be selected in ⁶C₃ =20 ways and can be assigned role in 3! = 6 ways
Hence total ways role to woman can be assigned =20 x 6 = 120
Girl can be P
There are 4 girls
Hence 4 ways
Boy can be supporting roles
There are 3 boys
Hence 3 ways
Total Ways = 30 x 120 x 4 x 3
= 43,200
The number of ways the roles can be cast is: 43200
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