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# There are 5 married couples and a group of three is to be

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Intern
Joined: 07 Aug 2003
Posts: 19
Location: USA
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There are 5 married couples and a group of three is to be [#permalink]  06 Dec 2003, 15:32
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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?
CEO
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Re: PS-Com [#permalink]  06 Dec 2003, 15:44
preyshi wrote:
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?

if you mean "Arrangements" , its a totally different question.

i assume ,you meant # of ways to select three people so that a couple in not there in a group.

Required answer = total # of ways - # of ways in which a couple are in a group.

1. Total # of ways = 10C3 ( 5 couples...ten people) = 120

2. # of ways a couple can be selected = 5C1 * 8C1 = 40 ways

Select one couple out of the five ..and select one person out of the rest
of the 8.

3. required answer = 120 - 40 = 80 ways

EDIT : thanks BG... correction made with bold part

Last edited by Praetorian on 07 Dec 2003, 05:08, edited 2 times in total.
Director
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Pret please note that : total arrangements 120. Arrangements with a couple are 40 (5C1 not 5C2, order is irrelevant ) so arrangements without couple are 80
Senior Manager
Joined: 12 Oct 2003
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I read the question itself in a diferent way.

i read it as "..a husband and wife may not be in ..." ... meaning husband and wife may be OR may not be.

same as in "I may not go there" .. it means I may OR may not go there.

Where am I going wrong here?
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