GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Jun 2019, 00:26

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
avatar
Joined: 12 Mar 2009
Posts: 271
GMAT ToolKit User
If there are four distinct pairs of brothers and sisters, th  [#permalink]

Show Tags

New post Updated on: 06 Jun 2014, 02:59
1
9
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

46% (00:25) correct 54% (00:28) wrong based on 136 sessions

HideShow timer Statistics

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
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 267
Re: gc test 2  [#permalink]

Show Tags

New post 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
Intern
avatar
Joined: 14 Apr 2008
Posts: 46
Re: gc test 2  [#permalink]

Show Tags

New post 01 Aug 2009, 05:45
4c3 for selececting 3 couples then for every three v have 2 chioces
4c3*2*2*2
Intern
Intern
avatar
Joined: 17 Jan 2010
Posts: 5
Re: gc test 2  [#permalink]

Show Tags

New post 26 Jan 2010, 05:47
Why are we multiplying 4 pair of siblings by 6C1?
Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 267
Re: gc test 2  [#permalink]

Show Tags

New post 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
Manager
avatar
Joined: 02 Oct 2009
Posts: 162
Re: gc test 2  [#permalink]

Show Tags

New post 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
Intern
avatar
Joined: 23 Feb 2011
Posts: 3
Re: gc test 2  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Sep 2009
Posts: 55716
Re: If there are four distinct pairs of brothers and sisters, th  [#permalink]

Show Tags

New post 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 \(C^3_4*2^3=32\).

Answer: C.

Similar questions to practice:
in-a-room-filled-with-7-people-4-people-have-exactly-87550-20.html
a-certain-junior-class-has-1-000-students-and-a-certain-58914.html
a-dog-breeder-currently-has-9-breeding-dogs-6-of-the-dogs-131992.html
three-pairs-of-siblings-each-pair-consisting-of-one-girl-136837.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-there-are-four-distinct-pairs-of-brothers-and-sisters-99992.html
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11396
Re: If there are four distinct pairs of brothers and sisters, th  [#permalink]

Show Tags

New post 18 Sep 2018, 19:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If there are four distinct pairs of brothers and sisters, th   [#permalink] 18 Sep 2018, 19:03
Display posts from previous: Sort by

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne