gmat-challenger wrote:A certain acting troupe is putting on a play that has four female roles and three male roles. If the troupe consists of ten actors, with an equal number of men and women, how many ways can the roles be assigned to the troupe, assuming each actor can only play one part?
a)604,800
b)50,400
c)7,200
d)180
e)50
3 male roles, 5 male actors:
Number of arrangements of 3 that can be made from 5 choices = 5*4*3 = 60.
4 female roles, 5 female actors:
Number of arrangements of 4 that can be made from 5 choices = 5*4*3*2 = 120.
Multiply the number of choices for the male roles with the number of choices for the female roles, we get:
60*120 = 7200.
The correct answer is
C.
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