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Mgmat_ps

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Intern
Joined: 02 Oct 2006
Posts: 39

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04 Feb 2007, 09:02
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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?

A)20%
b)30%
c)40%
d)50%
e)60%
Director
Joined: 13 Nov 2003
Posts: 789
Location: BULGARIA

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04 Feb 2007, 09:10
Hi
the number of subcom with M and A is 4
The number of subcom that include M and 2 other members is 10
the required prob is 4/10
Intern
Joined: 20 Jan 2007
Posts: 17

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04 Feb 2007, 10:55
The number of possible cases is the number of subcomitees that include michael, so we have:

Possible=MÂ·5Â·4 = 20 cases
Possible cases including Michael and Anthony= MÂ·AÂ·4 = 4 cases

Therefore,

The ratio is = 4/20=1/5=20%
Senior Manager
Joined: 19 Jul 2006
Posts: 358

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04 Feb 2007, 10:59
number of subcom with M and A is 4
number of subcom that include M and 2 other members = 1*5*4 = 20

(4/20)*100= 20%
Manager
Joined: 01 Oct 2006
Posts: 242

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04 Feb 2007, 11:08
No of possible 2 3-person committees = 6C3 = 20
Possible ways in which Mike and Anthony are always together = 4
(If Mike and Anthony are always together, then the third member can be one of the remaining 4)

% = 4/20 = 20%
Intern
Joined: 02 Oct 2006
Posts: 39

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05 Feb 2007, 01:57
BG is right and the oa is c)40%. BG can you plz explain it as am still trying to figure it out.
Director
Joined: 13 Nov 2003
Posts: 789
Location: BULGARIA

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05 Feb 2007, 02:28
Hi Lali,

from the posts of the other members, i see that we all reach the same result about the number of subcoms with M&A together-4.
All possible subcoms that include M are , we take M, and we need 2 more people 5C2=10.
Think it helps
Senior Manager
Joined: 05 Oct 2006
Posts: 266

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05 Feb 2007, 06:09
the qus was a nice trap.
"of all the possible subcommittees that include Michael also include Anthony?"

so michael has to be in both cases.

lali 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?

A)20%
b)30%
c)40%
d)50%
e)60%
Re: Mgmat_ps   [#permalink] 05 Feb 2007, 06:09
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