Couples

**metal_rulz** · 01-30-2004, 10:38 PM

There are 5 married couples and a group of three is to be formed out of them; how many arrangements are there if a husband and wife may not be in the same group?

**shivani_bha** · 02-02-2004, 10:40 AM

Hi Testmagicians,

Am not sure, so correct me if I'm wrong.

There are 10 people, 5 husbands and 5 wives. 3 people can be chosen as 2 Husbands and 1 wife or 2 wives and 1 husband. This can be done in 5C2*3C1 (excluding those two husbands wives) + 5C2*3C1

Hope this helps

Shivani

**shivani_bha** · 02-02-2004, 10:53 AM

Hi Testmagicians,

I would like to add to the above post 3 people can also be chosen as 3 husbands or 3 wives (3C1 + 3C1) = 6 additional ways

Shivani

**DaffyDuck** · 02-02-2004, 05:11 PM

Hi,

In my opinion, the question can be solved in the following manner:
Husband and wife not in same group = Total no. of arrangements - (Husband and Wife together)

Since there are 10 people --> Total = 10C3 = 120

Husband and Wife together in group = (Choose 1 couple out of 5 accounting for 2 earthlings in the group) x (Choose one person out of the remaining 8 people)
-->5C1 x 8C1 = 40

Ans= 120 - 40 = 80

**dig12us** · 02-02-2004, 06:13 PM

what is the correct ans

**thefish** · 02-02-2004, 08:13 PM

Is the question says that a group of 3 couples needs to be formed or a group of 3 people?

Question seems a little vague to be an official type question

**gmatfordays** · 02-02-2004, 11:23 PM

I think the question is asking for 3 people to form a group. So how many 3 person groups can be arranged so that no married couple is within the same 3 person group.