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Anthony and Michael sit on the six-member board of directors

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Senior Manager
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Anthony and Michael sit on the six-member board of directors [#permalink] New post 16 Aug 2006, 10:51
Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?


20%
30%
40%
50%
60%
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 [#permalink] New post 16 Aug 2006, 13:08
A) 20%

The number of ways that Michael and Anthony will be in one 3-member group is the number of ways the other 3-member group can be formed without either of them.

So we have 4 choices, and the number of groups that can be formed is ( 4*3*2). Th total number of ways a group of 3 can be formed is (6*5*4). Probability = 1/5.
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 [#permalink] New post 16 Aug 2006, 20:56
paddyboy wrote:
Th total number of ways a group of 3 can be formed is (6*5*4). Probability = 1/5.


Paddyboy, I beg to differ with you.
The order of members within the group is not significant. Thus, the number of 3 member groups that can be formed will be 6C3 = 20 and not 6P3.
Also, if Anthony and Michael are to come in 1 group together, the number of groups that can be formed are 5C3 = 5C2 = 10.
Hence, %age = 10/20 = 50%.
IMO answer should be (D).

Am very weak in probability and permutation-combinations. So kindly let me know if there is an issue with my approach to this problem.
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 [#permalink] New post 16 Aug 2006, 20:59
Popular one.
Answer is 40%

see my explanation
http://www.gmatclub.com/phpbb/viewtopic.php?t=33483
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

  [#permalink] 16 Aug 2006, 20:59
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Anthony and Michael sit on the six-member board of directors

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