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A play has two roles for men and four roles for women. If five men and

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A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 02:00
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A play has two roles for men and four roles for women. If five men and 12 women try out for these parts, in how many different ways can the director choose people for the roles?

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237,600



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volcanictempest78
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Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 09:39
Kindly explain shouldn't the answer be 5c2 * 12c4 = 4950
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Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 09:48
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The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.
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Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 10:00
Carcass wrote:
The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.


I get this answer when I account for arrangement in 5c2* 2! * 12c4 *4!
but this is not asking for arrangement, question mentions how director can chose among the 5 men for the two roles..in addition to this since it is not mentioned the roles are distinct won't we be double counting
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Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 11:31
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volcanictempest78 wrote:
Carcass wrote:
The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.


I get this answer when I account for arrangement in 5c2* 2! * 12c4 *4!
but this is not asking for arrangement, question mentions how director can chose among the 5 men for the two roles..in addition to this since it is not mentioned the roles are distinct won't we be double counting


Sir

the explanation above is a fundamental counting principle

You must choose five men and then four. you do not have any sort of constraint

The same for the women

Regards
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Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 12:09
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volcanictempest78 wrote:
Carcass wrote:
The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.


I get this answer when I account for arrangement in 5c2* 2! * 12c4 *4!
but this is not asking for arrangement, question mentions how director can chose among the 5 men for the two roles..in addition to this since it is not mentioned the roles are distinct won't we be double counting


I agree. The author could have added a few extra words to inform us that the 6 roles are distinct/different.
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Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 13:25
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For me, there is not so much room for misinterpretation...................
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Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   06 Apr 2022, 23:55
Carcass wrote:
The first male role can be filled by any of the five men, and the second by any of the remaining 4, for a total of 5 * 4 = 20 choices. Similarly, there are 12 options for the first female role, 11 for the next, 10 for the third, and 9 for the last. The total number of possibilities is thus 5 * 4 * 12 * 11 * 10 * 9 = 237,600.

Would you please enlighten me why it is not 5*4 + 12*11*10*9 ?
Aren't men and female roles are two separate entities?
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Re: A play has two roles for men and four roles for women. If five men and [#permalink] New post   07 Apr 2022, 02:58
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A play has two roles for men and four roles for women

and = multiplication
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