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 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
Learn More:
7. Find the number of ways of drawing 9 ballsfrom a bag that has 6 ...
https://brainly.in/question/13121350
Number of ways to paint Send Feedback You have to paint a two ...
https://brainly.in/question/29725471
A sleeper coach in a train has 8 lower berths, and 10 upper berths ...
https://brainly.in/question/13468915