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Probability and combinations- committee

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Probability and combinations- committee

by venmic » Tue May 10, 2011 8:32 pm
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%

40

Please i need a easy approach to this

Thx
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by manpsingh87 » Tue May 10, 2011 10:42 pm
venmic 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%

40

Please i need a easy approach to this

Thx
let member be a,b,c,d,e,f; total no. of ways of selecting 3 members be 6C3;= 20;
if we observe we will notice that whenever we select first members of a group last three are selected automatically, for example; if we selecte abc, def are selected automatically, and if we select def, abc is formed automatically, and since def,abc is similar as abc,def i.e. we have counted our group twice, so we need to halved the total no. of ways of selecting the group= 1/2*20=10;

since micheal and anthony will always be together, their third partner can be selected from any of the remaining 4 members in 4C1 ways= 4; i.e. out of 10 committees,or groups that are form 4 contains anthony and micheal as its members hence required percentage= (4/10)*100=40% hence C
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by Anurag@Gurome » Tue May 10, 2011 10:47 pm
venmic 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%

40

Please i need a easy approach to this

Thx

Solution:
The number of subcommittees having Michael is 5C2 = 10.
The number of subcommittees having both Michael and Anthony is 4C1 = 4.
So, required % is 4/10 * 100 = 40%
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by Brent@GMATPrepNow » Sat Oct 19, 2019 2:10 pm
venmic 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%
Let's assume that we're creating subcommittees.
We want to place 6 people in the following spaces:
_ _ _ | _ _ _

First, we place Michael in one subcommittee; it makes no difference which one:
M _ _ | _ _ _

Now place Anthony.
We can see that there are 5 spaces remaining. 2 spaces are on the same subcommittee as Michael.
So the probability that they are on the same subcommittee is 2/5 = 40%
In other words, 40% of the possible outcomes feature Anthony and Michael on the SAME committee

Answer: C

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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