Anthony and Michael sit on the six-member board of directors : Quant Question Archive [LOCKED]
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# Anthony and Michael sit on the six-member board of directors

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Manager
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Anthony and Michael sit on the six-member board of directors [#permalink]

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03 Jul 2007, 18:31
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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%

Please explain the approach.I have no clues how to solve these problems
Senior Manager
Joined: 04 Jun 2007
Posts: 346
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Kudos [?]: 29 [0], given: 0

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03 Jul 2007, 18:55
dreamgmat1 wrote:
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%

Please explain the approach.I have no clues how to solve these problems

There can be 4 sub-committees that contain both Michael and Anthony (4C1).
Total number of sub-committees = 6C3 = 20

Therefore, required percentage = 4/20 * 100 = 20% (A).
Director
Joined: 09 Aug 2006
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03 Jul 2007, 20:20
sumande wrote:
dreamgmat1 wrote:
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%

Please explain the approach.I have no clues how to solve these problems

There can be 4 sub-committees that contain both Michael and Anthony (4C1).
Total number of sub-committees = 6C3 = 20

Therefore, required percentage = 4/20 * 100 = 20% (A).

I guess here is a trap. It says 2 committees each of 3 members is to be formed and not a committee of just 3 out of 6 people. So can we say the total number of committees are 6C3 = 20 ? I doubt it.

I am puzzled further..
Director
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04 Jul 2007, 03:54
20%

The total number of possible sub-committees = 6C3 = 20

Number of sub-committees having Michael and Anthony together = 4
Manager
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04 Jul 2007, 05:05
well...

we have 6 chairs

_ _ _ _ _ _ and M and A are in

if this comitee is splited in 2 of 3 the possible outcomes would be:

M A _ /_ _ _
M _ _/ A _ _
A _ _/M _ _
_ _ _/M A _

it does not matter the order in the group, just if M and A stays together in one of them.

The questions says: "what percent of all the possible subcommittees that include Michael also include Anthony"

my answer is 2/4 or 50%

so in 4 groups that include M just 2 of them include Anthony...

On the other side if we prime for order, M can be in 6C3, or 20 outcomes
M cane be 4/20 or 20%

MXA/ZHF
XMF/ZHA
XMZ/HAF
.................

what's the OA?
Manager
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04 Jul 2007, 07:43
The OA is 40 %

Heres the explanation

If Michael must be on each of the three-person committees that we are considering, we are essentially choosing people to fill the two remaining spots of the committee.

The number of different combinations of two-person committees from a group of 5 board members is
5! / (3!2!) = 10. Therefore there are 10 possible committees that include Michael.

Out of these 10 possible committees, of how many will Anthony also be a member? If we assume that Anthony and Michael must be a member of the three-person committee, there is only one remaining place to fill. Since there are four other board members, there are four possible three-person committees with both Anthony and Michael. Of the 10 committees that include Michael, 4/10 or 40% also include Anthony.
Director
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04 Jul 2007, 07:52
Good question. There was a trap. I could have read it well.
Director
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04 Jul 2007, 08:23
Nice question, what is the source?
Manager
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04 Jul 2007, 09:31
hell!!!!!!! at least no one got it right ...good one!!!!!!!!
Senior Manager
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04 Jul 2007, 09:38
andrehaui wrote:
hell!!!!!!! at least no one got it right ...good one!!!!!!!!

That is encouraging !!
Good question !!
04 Jul 2007, 09:38
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