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A department of ten people - five men and five women - needs to send a

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Bunuel
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A department of ten people - five men and five women - needs to send a [#permalink] New post   17 Jul 2016, 08:49
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A department of ten people - five men and five women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?

A. 100
B. 126
C. 200
D. 252
E. 288
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C
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abhimahna
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Re: A department of ten people - five men and five women - needs to send a [#permalink] New post   17 Jul 2016, 09:08
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Bunuel wrote:
A department of ten people - five men and five women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?

A. 100
B. 126
C. 200
D. 252
E. 288


We are given 5 men and 5 Women, out of which we need to select 5 People such that no more than 3 of any gender are selected.
So, We can have Either 3 Men + 2 Women Selected or 2 Men + 3 Women Selected.

Thus, Number of ways for selecting 3 Men + 2 Women = 5C3 * 5C2 = 10*10=100

AND Number of ways for selecting 2 Men + 3 Women = 5C2 * 5C3 = 10*10=100

Thus, total ways to get the distinct groups will be 100+100=200.

Hence, Ans will be C.
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Re: A department of ten people - five men and five women - needs to send a [#permalink] New post   17 Jul 2016, 09:10
Bunuel wrote:
A department of ten people - five men and five women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?

A. 100
B. 126
C. 200
D. 252
E. 288


The possible combinations are
2 Men and 3 women

5!/2!3! *5!/3!2!= 100

or 3 men and 2 women
5!/2!3! *5!/3!2!= 100

100+100= 200 possible combinations

C is the answer
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Re: A department of ten people - five men and five women - needs to send a [#permalink] New post   17 Jan 2017, 15:33
Its answer C

There are only 2 options: 3 w and 2 m or 2 w and 3 m

Recall combinations formula

N!/(K!)(N-K)!, where N is the total set and k the chosen object

3 w and 2 m
Choose from 5 women, 3 = 5!/3!*2!= 4*5/1*2= 20/2 = 10

Choose from 5 men, 2= 5!/2!*3!= 10

10*10 = 100 and equivalent for 2 w and 3 m = 10*10 = 100, so in sum 200
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Re: A department of ten people - five men and five women - needs to send a [#permalink] New post   17 Jan 2017, 21:37
Bunuel wrote:
A department of ten people - five men and five women - needs to send a team of five to a conference. If they want to make sure that there are no more than three members of the team from any one gender, how many distinct groups are possible to send?

A. 100
B. 126
C. 200
D. 252
E. 288




total-10C5
4 men 1 women = 5c4 * 5c1 * 2( multiplied by 2 as we have possible 4 women 1 men team)
5 women=1
5 men=1

10c5-5c4 * 5c1 * 2-2
252-50-2
=200
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Re: A department of ten people - five men and five women - needs to send a [#permalink] New post   15 May 2023, 02:41
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Re: A department of ten people - five men and five women - needs to send a [#permalink]
15 May 2023, 02:41
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