BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Combinations

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 19
Joined: Thu Jul 29, 2010 2:12 am

Combinations

by shilpaqueen » Sat Oct 30, 2010 12:59 am
Anita and Minu sit on the eight-member board of directors for company X. If the board is to be split up into 2 four-person subcommittees, what approximate percent of all the possible subcommittees that include Michael also include Anthony?


I think the answer to this should be 21 % but not sure ...am i correct?


This is how I arrived at it

Total number of possible 4 member committee = 70 ( 8C4)
Total number that have both Anita and Minu = 15
Thus percentage (15/70)X 100= 21.42% or 21 %
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Oct 30, 2010 3:01 am
shilpaqueen wrote:Anthony and Michael sit on the eight-member board of directors for company X. If the board is to be split up into 2 four-person subcommittees, what approximate percent of all the possible subcommittees that include Michael also include Anthony?


I think the answer to this should be 21 % but not sure ...am i correct?


This is how I arrived at it

Total number of possible 4 member committee = 70 ( 8C4)
Total number that have both Anita and Minu = 15
Thus percentage (15/70)X 100= 21.42% or 21 %
Careful! The question is asking:

Out of all the possible subcommittees that include Michael, what percent would also include Anthony?

First we need to determine the number of committees that could include Michael. Michael needs to be combined with 3 people from the remaining 7: 7C3 = 35.

If Michael and Anthony are both to serve on the committee, they need to be combined with 2 people from the remaining 6: 6C2 = 15.

P = 15/35 = 3/7 ≈ 40%.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Junior | Next Rank: 30 Posts
Posts: 19
Joined: Thu Jul 29, 2010 2:12 am

by shilpaqueen » Sat Oct 30, 2010 3:19 am
Basically if the question said what percentage of the total sub-committee both Michel and Antony are part of then 21% would be the correct answer right??
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Oct 30, 2010 3:29 am
shilpaqueen wrote:Basically if the question said what percentage of the total sub-committee both Michel and Antony are part of then 21% would be the correct answer right??
Yes indeed.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 am
Thanked: 29 times
Followed by:3 members

by diebeatsthegmat » Mon Nov 01, 2010 9:38 am
GMATGuruNY wrote:
shilpaqueen wrote:Anthony and Michael sit on the eight-member board of directors for company X. If the board is to be split up into 2 four-person subcommittees, what approximate percent of all the possible subcommittees that include Michael also include Anthony?


I think the answer to this should be 21 % but not sure ...am i correct?


This is how I arrived at it

Total number of possible 4 member committee = 70 ( 8C4)
Total number that have both Anita and Minu = 15
Thus percentage (15/70)X 100= 21.42% or 21 %
Careful! The question is asking:

Out of all the possible subcommittees that include Michael, what percent would also include Anthony?

First we need to determine the number of committees that could include Michael. Michael needs to be combined with 3 people from the remaining 7: 7C3 = 35.

If Michael and Anthony are both to serve on the committee, they need to be combined with 2 people from the remaining 6: 6C2 = 15.

P = 15/35 = 3/7 ≈ 40%.
hi,
so does it mean that the PS just asks us to find the percentage of the possibility that there will be A / the group of anthony and michael?
Top
Master | Next Rank: 500 Posts
Posts: 134
Joined: Sun Jul 25, 2010 5:22 am
Thanked: 1 times
Followed by:2 members

by gmatusa2010 » Tue Nov 02, 2010 3:27 am
I know this is not relevant to the question but how would you calculate the total number of subcomittees? I though it said 2 4-people subcomittee and not 1 4-people subcomittee out of 8 people.

(8!/4!4!)/(2!)?

Subcomittee 1:

Team 1= ABCD
Team 2= EFGH

Thats one set right?

Team1= EFGH
Team 1= ABCD (this is double counting)

GMATGuruNY, can actually solve this problem under the assumption that the questions asks for the % Total that Michael and Anthony part of and under, I guess my interpretation of what subcomittee means. (Let me rephrase the question as I understood, how many ways to arrange 8 people in 2 teams of 4. )



GMATGuruNY wrote:
shilpaqueen wrote:Basically if the question said what percentage of the total sub-committee both Michel and Antony are part of then 21% would be the correct answer right??
Yes indeed.
Top
User avatar
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Tue Sep 28, 2010 9:19 am
Thanked: 3 times
Followed by:1 members

by waltz2salsa » Tue Nov 02, 2010 11:49 pm
Anthony and Michael sit on the eight-member board of directors for company X. If the board is to be split up into 2 four-person subcommittees, what approximate percent of all the possible subcommittees that include Michael also include Anthony?
lets deal the probability question, the probability way ;)

lets assume we have two committees a and b (each with 4 members each)

probability that Michael lands in 'a' is = 1/2 ( = 4/8)
Now, probability that Anthony lands in 'a', given Michael is already there = 3/7 ( total places = 7 left, but in 'a' only 3 left)

Also, keep in mind that Michael could even land in 'b originally, so our final would be

probability that Anthony lands in 'a' or 'b', given Michael is already there = 2* ( 1/2 * 3/7) = 3/7

For percentage , multiply by 100 ;)
Top
Post new topic Post Reply
• Page 1 of 1