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

Question

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

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

abhimahna · Answer

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.

Divyadisha · Answer

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

JFromm · Answer

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

sobby · Answer

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

bumpbot · Answer

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

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