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

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Senior Manager
Joined: 23 Aug 2003
Posts: 461
Location: In the middle of nowhere
There are 5 married couples and a group of three is to be [#permalink]

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30 Jan 2004, 18:19
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

* 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?
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

Manager
Joined: 25 Jan 2004
Posts: 92
Location: China

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30 Jan 2004, 18:25
C(10,3) = 120 (with no restrictions)

# ways to have a couple in the group of 3 = 5 * 8 = 40

Answer, I guess, is = 80
Manager
Joined: 26 Dec 2003
Posts: 227
Location: India

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30 Jan 2004, 18:45
Hmmmmmm I am getting 560.
Intern
Joined: 25 Jan 2004
Posts: 28
Location: Redwood City, USA

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30 Jan 2004, 20:42
Hi, I am coming over from the 'other' test prep site. Found this question over there as well.

I agree with Zhung Gazi on this one.

10c3 yields 120 with no restrictions.

figuring how many groups can be formed with couples being apart of them, would be 5 * 8 or 40.

120 - 40 yields 80 distinct groups.
Intern
Joined: 13 Aug 2003
Posts: 26
Location: DELHI

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04 Feb 2004, 04:25
Total Combinations :- 10C3=120
Ways in which one couple can be involved in the group is = 8
so for all couples it comes out to be = 5*8= 40

So total ways in which no couple is involved in the group = 120-40 = 80
Manager
Joined: 16 Jan 2004
Posts: 64
Location: NJ

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04 Feb 2004, 10:44
I guess the way to solve this would be

total-# of ways a husband and wife can be in a group

total - 10C3 = 120

Ways in which couple can be a part of the group 5*8 = 40

5 Couples we can choose 1 = 5C1 = 5
1 Person from the remaining 8 = 8C1 = 8

Ans : 120-40.

Please correct me If I am wrong
Senior Manager
Joined: 23 Aug 2003
Posts: 461
Location: In the middle of nowhere

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04 Feb 2004, 21:37
Pakoo u r right...

Vivek.
_________________

"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

04 Feb 2004, 21:37
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# There are 5 married couples and a group of three is to be

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