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# If there are four distinct pairs of brothers and sisters, th

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Senior Manager
Joined: 12 Mar 2009
Posts: 285
If there are four distinct pairs of brothers and sisters, th  [#permalink]

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Updated on: 06 Jun 2014, 02:59
1
6
00:00

Difficulty:

65% (hard)

Question Stats:

48% (00:25) correct 52% (00:25) wrong based on 126 sessions

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If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it?

A. 8
B. 24
C. 32
D. 56
E. 192

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-there-are-four-distinct-pairs-of-brothers-and-sisters-99992.html

Originally posted by vaivish1723 on 31 Jul 2009, 23:47.
Last edited by Bunuel on 06 Jun 2014, 02:59, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
Joined: 25 Jun 2009
Posts: 279

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01 Aug 2009, 02:46
vaivish1723 wrote:
If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it?

8
24
32
56
192

Oa is

pl explain

Total no. of combinations = 8C3= 56
Now lets take the case when we have one sibling in the committee. Say 1 pair then the no. of combination 6C1 X 4= 24 ( as we have 4 pair of siblings)

No. of ways when we don't have siblings in it = 56-24= 32
Intern
Joined: 14 Apr 2008
Posts: 48

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01 Aug 2009, 05:45
4c3 for selececting 3 couples then for every three v have 2 chioces
4c3*2*2*2
Intern
Joined: 17 Jan 2010
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26 Jan 2010, 05:47
Why are we multiplying 4 pair of siblings by 6C1?
Senior Manager
Joined: 25 Jun 2009
Posts: 279

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26 Jan 2010, 10:56
bhumika wrote:
Why are we multiplying 4 pair of siblings by 6C1?

We are trying to calculate the no. of ways in which there is one pair and one other.

so there are 6C1 ways of choosing one guy who can be paired with one pair.

Now there are 4 pairs and total no. of ways = 6C1 x 4

I hope that helps..!
Manager
Joined: 02 Oct 2009
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29 Jan 2010, 22:51
keeping it simple (b1,s1),(b2,s2),(b3,s3),(b4,s4),
1 Pair produces 2 possible wasy between (b,s) with total picks is 3; 2*2*2
Then amount 4 unique pairs it can for another 4 times for unique pairing 8*4=32... brings you back to combinatorics... being a quicker calculation then the above logic...
Intern
Joined: 23 Feb 2011
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08 May 2011, 07:15
2
1
First find the total number of combinations without any constraints, which is 8c3 = 56 (since we're looking to make a committee of 3 people out of 8 and order doesn't matter).

Then, find out all the ways in which you would have a sibling on the committee. Let's look at one sibling pear (Brother, Sister). The number of ways they can both get on the panel is 2c2 * 6 (the six represents the 3rd person on the committee, as there are 6 people left to choose from for the last spot), which gets you 6 combinations. Multiply that 6 by 4 to incorporate the 4 different pairs of siblings.

Using the info we've calculated, the total number of combinations is 56 - 24 = 32.
Math Expert
Joined: 02 Sep 2009
Posts: 50042
Re: If there are four distinct pairs of brothers and sisters, th  [#permalink]

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06 Jun 2014, 03:01
If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it?

A. 8
B. 24
C. 32
D. 56
E. 192

As committee shouldn't have siblings in it, then a pair can send only one "representative" to the committee. # of ways to choose which 3 pairs of brothers and sisters should send one "representative" to the committee is $$C^3_4$$ (choosing 3 pairs which will be granted the right to send one "representative" to the committee);

But each of these 3 pairs can send 2 persons to the committee either a brother or a sister: $$2*2*2=2^3$$;

So total # of ways is $$C^3_4*2^3=32$$.

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OPEN DISCUSSION OF THIS QUESTION IS HERE: if-there-are-four-distinct-pairs-of-brothers-and-sisters-99992.html
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Re: If there are four distinct pairs of brothers and sisters, th  [#permalink]

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18 Sep 2018, 19:03
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Re: If there are four distinct pairs of brothers and sisters, th &nbs [#permalink] 18 Sep 2018, 19:03
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