GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 03 Aug 2020, 21:18

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

There are four distinct pairs of brothers and sisters. In how many way

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
SVP
SVP
User avatar
Joined: 21 Jan 2007
Posts: 1856
Location: New York City
There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 02 Dec 2007, 13:57
10
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

65% (00:43) correct 35% (02:07) wrong based on 53 sessions

HideShow timer Statistics

There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65765
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 08 Jul 2013, 21:41
2
5
Maxirosario2012 wrote:
What would be the ansmer if instead of a committee of 4 we would need a committee of 3?
64 possible committees?

\(2^4 * C^4_3\) = 16*4 = 64

And a committee of 2? 96?
\(2^4 * C^4_2\) = 16*6 = 96


There are four distinct pairs of brothers and sisters.

A. In how many ways can a committee of 4 be formed and NOT have siblings in it?
2^4

B. In how many ways can a committee of 3 be formed and NOT have siblings in it?
\(C^3_4*2^3=32\).
Check here: if-there-are-four-distinct-pairs-of-brothers-and-sisters-99992.html

C. In how many ways can a committee of 2 be formed and NOT have siblings in it?
\(C^2_4*2^2=24\).

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
if-there-are-four-distinct-pairs-of-brothers-and-sisters-99992.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

Hope it helps.
_________________
Most Helpful Community Reply
Senior Manager
Senior Manager
avatar
Joined: 14 Aug 2007
Posts: 452
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 11 Mar 2009, 22:28
4
2
another method

The commitee of 4 , NOT having siblings can be formed in following ways:

0 Sisters and 4 brothers = 4C4 =1
+
1 sister and 3 brothers = 4C1*3C3 = 4 [ 3C3 because selected sister's brother can not be among 3 bros]
+
2 sisters and 2 brothers = 4C2* 2C2 = 6 [ again 2C2 because brothers of 2 selected sisters can not be on commitee]
+
3 sisters and 1 brother = 4C3* 1C1 = 4 [ only one brother whose sister is not on commitee can be selected]
+
4 sisters and 0 brothers = 4C4 = 1

= 16 total ways.
General Discussion
Intern
Intern
avatar
Joined: 28 Aug 2007
Posts: 37
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 04 Dec 2007, 06:26
3
2
bmwhype2 wrote:
There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?


8*6*4*2 / 4! = 384/24 = 16

Just brute force it, on first place you can put 8, on second you can put 6 (excluding 1 sibling) on third you can put 4 (exclude) 2 siblings... then divide by the number of permutations as position doesnt matter.

Whats the answer?
SVP
SVP
User avatar
Joined: 21 Jan 2007
Posts: 1856
Location: New York City
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 16 Dec 2007, 21:28
1
i'm not even sure of the answer. maybe walker can help out.

4 pairs = 4*2 = 8 people total

8C4 = 8!/4!4! = 70 total outcomes

Total – unfavorable = favorable

Unfavorable outcomes
Assuming one pair of twins in the committee, we have two spaces left. Since we plugged a pair of twins in the committee, we have 8-2= 6 people to fill 2 spaces.

6C2 = 6!/2!4! = 15 ways to fill the two remaining slots

We only filled the slots with one pair, and we have to account for arrangements of the pairs. Now, we have 4 pairs. 4*15= 60 total arrangements

When we place members into the remaining slots, there may be an additional set of twins. There are 2 remaining slots to which we can fit a pair of twins. If it were one remaining slot, we cannot fit a pair of twins, so we wouldn’t have to account for duplicates.

Now we account for the number of duplicates.
# of duplicates = Total arrangements - # of unique combinations

To find the # of duplicates of twins, we need treat a pair of twins as one unit.
This means the 4 slots are really 2 slots.

Total ways of arranging four pairs of twins in two slots
4P2 = 4*3 = 12 total ways

Total # of unique combinations
Choosing two pairs out of 4 pairs
= 4C2
= 6
Therefore, # of duplicates = 12 - 6 = 6 duplicates

70 – 60 + 6 = 16
VP
VP
User avatar
Joined: 07 Nov 2007
Posts: 1060
Location: New York
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 25 Aug 2008, 13:16
4
bmwhype2 wrote:
There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?


\(= (8C1*6C1*4C1*2C1)/ 4!\)
\(= 16\)
Intern
Intern
avatar
Joined: 24 Aug 2009
Posts: 3
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 28 Aug 2009, 03:25
5
The four distinct pairs of brothers and sisters:

Aa Bb Cc Dd

We have to choose one from each set. We can do it:
2 * 2 * 2 * 2 = 16 ways
Manager
Manager
avatar
Joined: 27 Oct 2008
Posts: 125
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 27 Sep 2009, 20:58
1
There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?

Soln:
2C1 * 2C1 * 2C1 * 2C1 = 16 ways
Intern
Intern
avatar
Joined: 11 Sep 2009
Posts: 46
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 13 Dec 2009, 02:41
3
2
8 * 6 * 4 *2 / 4! = 16

Note that 8 * 6 * 4 *2 create a duplicate such as ABCD and BACD. Thus, we need to cancel out the duplicates by dividing 4! (there are 4! ways to shuffle the committee)
Manager
Manager
User avatar
Joined: 02 Apr 2012
Posts: 58
Location: United States (VA)
Concentration: Entrepreneurship, Finance
GMAT 1: 680 Q49 V34
WE: Consulting (Consulting)
GMAT ToolKit User Reviews Badge
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 08 Jul 2013, 16:42
What would be the ansmer if instead of a committee of 4 we would need a committee of 3?
64 possible committees?

\(2^4 * C^4_3\) = 16*4 = 64

And a committee of 2? 96?
\(2^4 * C^4_2\) = 16*6 = 96
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65765
Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

Show Tags

New post 14 Aug 2016, 04:42
GMAT Club Bot
Re: There are four distinct pairs of brothers and sisters. In how many way   [#permalink] 14 Aug 2016, 04:42

There are four distinct pairs of brothers and sisters. In how many way

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





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