Math, asked by SabrinaAna, 4 months ago

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

Answered by amitnrw
0

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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