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# There are four distinct pair of brothers and sisteres. In

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Current Student
Joined: 04 Nov 2006
Posts: 132
Followers: 1

Kudos [?]: 29 [0], given: 8

There are four distinct pair of brothers and sisteres. In [#permalink]  10 Nov 2006, 04:25
There are four distinct pair of brothers and sisteres. In how many ways can a committee of three be formed and not have siblings in it?

8
24
32
56
80

Pls explain how u arrived at the answer also.
Senior Manager
Joined: 23 Jun 2006
Posts: 387
Followers: 1

Kudos [?]: 311 [0], given: 0

first choose which three (out of 4) pairs, have a representative in the committee (4 ways to do that... you can think of it as which pair doesn't have....)
now each pair can send, independently, 1 out of 2 possible representative.
so we have 2*2*2 = 8 possible committees once the three pairs are chosen.

since choosing the three pairs, and choosing the committee out of the given three pairs can be done independently... jut multiply it altogether to get 32

alternatively (i.e. what i would do on test day) just count.
for pairs 1,2,3: we have aaa,aab,aba,abb,baa,bab,bba,bbb
for pairs 1,2,4: aaa,aab,aba,abb,baa,bab,bba,bbb
now you can see that for each choices of pair you have 8 options. you have 4 choices of pairs and get 32 options altogether.

amit.
Director
Joined: 05 Feb 2006
Posts: 899
Followers: 1

Kudos [?]: 54 [0], given: 0

B....

Simply pick all opportunities:

AA
BB
CC
DD

ABC=3!
ACD=3!
ABD=3!
BCD=3!

Total 24....
Manager
Joined: 04 May 2006
Posts: 173
Location: paris
Followers: 1

Kudos [?]: 9 [0], given: 0

8C3 -4*6C,1

Total possibilities of 8 people taken by 3 minus the pairs of siblings, 4 pairs *6 other people

56-24 =32
_________________

time is not on my side

Intern
Joined: 02 Aug 2006
Posts: 23
Location: NYC
Followers: 0

Kudos [?]: 0 [0], given: 0

ugo_castelo wrote:
8C3 -4*6C,1

Total possibilities of 8 people taken by 3 minus the pairs of siblings, 4 pairs *6 other people

56-24 =32

32 too.

The first member can be chosen 8 ways, the second 6 ways and the third 4 ways. Then the total has to be divided by 3! as the order doesn't matter.
(8*6*4)/(3*2*1) = 32
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