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3 male roles, 5 male actors: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
The word assign suggests that it matters which particular actor is assigned to which particular role; otherwise, the problem would ask for the number of casts or combinations of actors that could be chosen. Whereas we choose a group of actors, we assign each actor to a role.force5 wrote:Hi Mitch my take is - 5c4*5c3=50
why would you want to use arrangement when you have to assign roles to the troupe which means choosing.
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