Question

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:

Answer 1

Answer:

Step-by-step explanation:

protagonists 6c1*6c1*4c1

antagonists 5c1*5c1

supporting roles 4c1*3c1

multiply all 6c1*6c1*4c1*5c1*5c1*4c1*3c1=43200

Answer 2

Given : 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

To Find : The number of ways the roles can be cast is:

Solution:

woman can be  protagonists  or antagonists

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  protagonists  , antagonists  , 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 protagonists  

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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