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

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

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04 Oct 2008, 06:11
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%
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Director
Joined: 12 Jul 2008
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Schools: Wharton
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04 Oct 2008, 07:25
amitdgr 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%

Total # of ways to choose = 6C3 = 20
Total number of committees with both Michael and Anthony = 4*1*1 = 4

20%
Intern
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04 Oct 2008, 09:13
1
KUDOS
The question is not "what percent of all the possible subcommittees include both Michael and Anthony?"

Then the answer would be 20%

The question is "what percent of all the possible subcommittees that include Michael also include Anthony?"

So you divide the number of possible combinations that include Michael and Anthony by the number of possible combinations that include Michael.

So, as zoinnk said there are 4 possible committees that include both Michael and Anthony.

I think it's easier to find the number of committees on which Michael does not appear at all, which would mean 5C3=10.
20-10 = 10 committees on which Michael appears.

4/10 = 40%
Director
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Schools: Wharton
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04 Oct 2008, 09:55
csvobo wrote:
The question is not "what percent of all the possible subcommittees include both Michael and Anthony?"

Then the answer would be 20%

The question is "what percent of all the possible subcommittees that include Michael also include Anthony?"

So you divide the number of possible combinations that include Michael and Anthony by the number of possible combinations that include Michael.

So, as zoinnk said there are 4 possible committees that include both Michael and Anthony.

I think it's easier to find the number of committees on which Michael does not appear at all, which would mean 5C3=10.
20-10 = 10 committees on which Michael appears.

4/10 = 40%

Sorry. Misread the question. You're right! +1
VP
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04 Oct 2008, 21:16
csvobo wrote:
The question is not "what percent of all the possible subcommittees include both Michael and Anthony?"

Then the answer would be 20%

The question is "what percent of all the possible subcommittees that include Michael also include Anthony?"

So you divide the number of possible combinations that include Michael and Anthony by the number of possible combinations that include Michael.

So, as zoinnk said there are 4 possible committees that include both Michael and Anthony.

I think it's easier to find the number of committees on which Michael does not appear at all, which would mean 5C3=10.
20-10 = 10 committees on which Michael appears.

4/10 = 40%

Even I did the same mistake as zoinnk ... Tricky words I guess ... zoinnk doesn't miss too many questions....

csvobo ... can you explain "to find the number of committees on which Michael does not appear at all, which would mean 5C3"

Thanks
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04 Oct 2008, 21:57

If Michael was sit, there is 5 positions left, in which only 2 for Michael's side. So 2/5 = 40%
VP
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04 Oct 2008, 22:17
lylya4 wrote:

If Michael was sit, there is 5 positions left, in which only 2 for Michael's side. So 2/5 = 40%

wow!! your method seems so much easier !!
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05 Oct 2008, 00:06
amitdgr 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%

Say there 6 members we need to form 3 member committee out of 3 members we know one is michael hence we need to select 2 out of 5
5C2 there 10 combinations

Now consider anthony and michael !!! hence select 1 out of 4 ,4C1
4 combitions

4/10 =2/5 0.4 =40%
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05 Oct 2008, 00:10
spriya wrote:
amitdgr 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%

Say there 6 members we need to form 3 member committee out of 3 members we know one is michael hence we need to select 2 out of 5
5C2 there 10 combinations

Now consider anthony and michael !!! hence select 1 out of 4 ,4C1
4 combitions

4/10 =2/5 0.4 =40%

_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Re: MGMAT - Combinatorics   [#permalink] 05 Oct 2008, 00:10
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