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combination/permutation - acting troupe

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by gmat-challenger » Sun Apr 03, 2011 3:13 am
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
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by GMATGuruNY » Sun Apr 03, 2011 3:53 am
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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by force5 » Sun Apr 03, 2011 4:01 am
my take is - 60*120 = 7200.
Last edited by force5 on Sun Apr 03, 2011 4:39 am, edited 1 time in total.
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by gmat-challenger » Sun Apr 03, 2011 4:08 am
Hi Mitch,

Answer is indeed C and I understand ur logic and that u are using permutation but the question is not saying that the roles are different. I mean, why would u assume that ABC is not the same as ACB? It is the same group of actors! Do you think such misleading and unclear questions can appear on the GMAT? Cause if u assume that the roles are the same and ABC=ACB, then answer is 5c4*5c3=50.

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Zlati
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by GMATGuruNY » Sun Apr 03, 2011 4:22 am
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.
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.

That being said, the GMAT writers likely would make it clear that all the roles are different.
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by gmat-challenger » Sun Apr 03, 2011 4:30 am
Great explanation! Thank you for clearing it up!
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by force5 » Sun Apr 03, 2011 4:38 am
Is there a better way to understand this difference? i think the only way is to read the question more carefully.

nice one none the less.
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