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

Author Message
Intern
Joined: 13 May 2012
Posts: 28
Schools: LBS '16 (A)
GMAT 1: 760 Q50 V41
Re: Anthony and Michael sit on the six member board of directors  [#permalink]

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19 Jul 2012, 12:16
1
I did it this way:

Total ways to choose 1st subcommittee = 6C3
Total ways to choose 2nd subcommittee = 1 (since only 3 people left)
Possible subcommittees = 1*6C3

Total ways to choose which out of the two subcommittee will Anthony and Michael be in= 2C1
Total ways to choose the remaining 1 person on that subcommittee = 4C1

P = (2C1*4C1)/(1*6C3) = 2/5 (40%)
Manager
Joined: 25 Jun 2012
Posts: 62
Location: India
WE: General Management (Energy and Utilities)
Re: Anthony and Michael sit on the six member board of directors  [#permalink]

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19 Jul 2012, 20:32
5
Totak ways to select 3 members from 6 members = 6C3 = 6!/3!*3! = 20
Now if the sis members are A,M,X1,X2,X3,X4 , take A & M together as a sing le unit Y.
Y = A,M, they can be selected as 2! ways = 2
Grups can be made as = YX1, YX2,YX3 & YX4 = 4
Total grups = 4*2=8

Now % is = 8/20*100=40% is the answer
Intern
Joined: 13 May 2012
Posts: 28
Schools: LBS '16 (A)
GMAT 1: 760 Q50 V41
Re: Anthony and Michael sit on the six member board of directors  [#permalink]

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20 Jul 2012, 05:57
manwiththeharmonica wrote:
I did it this way:

Total ways to choose 1st subcommittee = 6C3
Total ways to choose 2nd subcommittee = 1 (since only 3 people left)
Possible subcommittees = 1*6C3

Total ways to choose which out of the two subcommittee will Anthony and Michael be in= 2C1
Total ways to choose the remaining 1 person on that subcommittee = 4C1

P = (2C1*4C1)/(1*6C3) = 2/5 (40%)

Intern
Joined: 21 Sep 2010
Posts: 6
Re: Anthony and Michael sit on the six member board of directors  [#permalink]

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20 Jul 2012, 06:57
1
1
I agree with 40%. I used a pretty straightforward method that doesn't involve formulas:

MAC MCD MDE MEF
MAE MCF
MAF

These are the 10 possible 3-person subcommittees that include Michael. Only 4 of them include Anthony as well. 4/10=40%.
Non-Human User
Joined: 09 Sep 2013
Posts: 9427
Re: Anthony and Michael sit on the six member board of directors  [#permalink]

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01 Aug 2018, 06:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Anthony and Michael sit on the six member board of directors &nbs [#permalink] 01 Aug 2018, 06:42

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