Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 05 Jul 2015, 21:11

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Senior Manager
Joined: 17 Oct 2006
Posts: 439
Followers: 1

Kudos [?]: 12 [0], given: 0

Anthony and Michael sit on the six-member board of directors [#permalink]  08 Dec 2006, 08:16
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
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%
Senior Manager
Joined: 19 Jul 2006
Posts: 361
Followers: 1

Kudos [?]: 3 [0], given: 0

possible subcommittees that include Michael = 6C2
possible subcommittees that include Michael also include Anthony= 6C1

(6C1/ 6C2) * 100 = 40%
Senior Manager
Joined: 17 Oct 2006
Posts: 439
Followers: 1

Kudos [?]: 12 [0], given: 0

AK wrote:
possible subcommittees that include Michael = 6C2
possible subcommittees that include Michael also include Anthony= 6C1

(6C1/ 6C2) * 100 = 40%

Could you plz explain more. I am having difficulties following it. thanks
Senior Manager
Joined: 01 Sep 2006
Posts: 301
Location: Phoenix, AZ, USA
Followers: 1

Kudos [?]: 15 [0], given: 0

Re: DS - board of directors [#permalink]  08 Dec 2006, 15:27
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?

(1st case)
M and A both are already member means we need to find commitees with 1 person of rest of 4

4C1 i.ie 4 ways to form a comitee.
2 comitees i.e 8 ways

(2nd case)
5 people with 2 people comitee = 5C2=5*4/2=10
10 ways to form 1 comitte
togather 20 ways for 2 comittes

8/20= 2/5=40%
Senior Manager
Joined: 19 Jul 2006
Posts: 361
Followers: 1

Kudos [?]: 3 [0], given: 0

arjsingh1976 wrote:
AK wrote:
possible subcommittees that include Michael = 6C2
possible subcommittees that include Michael also include Anthony= 6C1

(6C1/ 6C2) * 100 = 40%

Could you plz explain more. I am having difficulties following it. thanks

Damager has explained well.. I did a mistake while puting it here
Intern
Joined: 24 Feb 2006
Posts: 48
Followers: 1

Kudos [?]: 0 [0], given: 0

Subcommittees that include Michael = 5C2 = 10 (select 2 from 5)
Subcommittees that include both Michael and Anthony= 4C1 = 4 (select 1 from 4; )
Manager
Joined: 08 May 2004
Posts: 158
Location: Pittsburgh
Followers: 1

Kudos [?]: 0 [0], given: 0

I am really confused by this ! It is not making sense
Manager
Joined: 08 May 2004
Posts: 158
Location: Pittsburgh
Followers: 1

Kudos [?]: 0 [0], given: 0

I am really confused
I am usually good with combo problems

How do we get to these ?

Subcommittees that include Michael = 5C2 = 10 (select 2 from 5)
Quote:
Subcommittees that include both Michael and Anthony= 4C1 = 4 (select 1 from 4; )
Intern
Joined: 25 Jul 2006
Posts: 44
Followers: 1

Kudos [?]: 4 [0], given: 0

how abt this...

one sub committee has 3 ppl nd u need to both anthony nd michael on it....

So..

3C2/6C2 or(+) 3C2/6C2...giving us 2/5 nd thereby 40%
Senior Manager
Joined: 01 Sep 2006
Posts: 301
Location: Phoenix, AZ, USA
Followers: 1

Kudos [?]: 15 [0], given: 0

jamesrwright3 wrote:
I am really confused
I am usually good with combo problems

How do we get to these ?

Subcommittees that include Michael = 5C2 = 10 (select 2 from 5)
Quote:
Subcommittees that include both Michael and Anthony= 4C1 = 4 (select 1 from 4; )

Comitee size =3
Michael has to be included. So he has already been chosen, i seat taken.
we need to find number of ways to choose members for remaing 2 seats.

Total number of people 6 - michel ( as he is already chosen = 5

Number of ways to choose 2 person out of 5 = 5C2= 5!/3!2!=5*4*3*2/( 3*2*2)===> 10

Similarly

When both michal and antony are chosen
total seats 3 . antony takes 1 snd micheal takes 1 . 1 seat remaining

Out of 6 people antony and michel alreasy chosen reming people 4

Number of ways to choose 1 peron out of 4 is 4C1=4!/3!=4
Senior Manager
Joined: 17 Oct 2006
Posts: 439
Followers: 1

Kudos [?]: 12 [0], given: 0

Damager wrote:
jamesrwright3 wrote:
I am really confused
I am usually good with combo problems

How do we get to these ?

Subcommittees that include Michael = 5C2 = 10 (select 2 from 5)
Quote:
Subcommittees that include both Michael and Anthony= 4C1 = 4 (select 1 from 4; )

Comitee size =3
Michael has to be included. So he has already been chosen, i seat taken.
we need to find number of ways to choose members for remaing 2 seats.

Total number of people 6 - michel ( as he is already chosen = 5

Number of ways to choose 2 person out of 5 = 5C2= 5!/3!2!=5*4*3*2/( 3*2*2)===> 10

Similarly

When both michal and antony are chosen
total seats 3 . antony takes 1 snd micheal takes 1 . 1 seat remaining

Out of 6 people antony and michel alreasy chosen reming people 4

Number of ways to choose 1 peron out of 4 is 4C1=4!/3!=4

Thanks. I got it now!
Manager
Joined: 08 May 2004
Posts: 158
Location: Pittsburgh
Followers: 1

Kudos [?]: 0 [0], given: 0

arjsingh1976 wrote:
Damager wrote:
jamesrwright3 wrote:
I am really confused
I am usually good with combo problems

How do we get to these ?

Subcommittees that include Michael = 5C2 = 10 (select 2 from 5)
Quote:
Subcommittees that include both Michael and Anthony= 4C1 = 4 (select 1 from 4; )

Comitee size =3
Michael has to be included. So he has already been chosen, i seat taken.
we need to find number of ways to choose members for remaing 2 seats.

Total number of people 6 - michel ( as he is already chosen = 5

Number of ways to choose 2 person out of 5 = 5C2= 5!/3!2!=5*4*3*2/( 3*2*2)===> 10

Similarly

When both michal and antony are chosen
total seats 3 . antony takes 1 snd micheal takes 1 . 1 seat remaining

Out of 6 people antony and michel alreasy chosen reming people 4

Number of ways to choose 1 peron out of 4 is 4C1=4!/3!=4

Thanks. I got it now!

Awesome explanation
Too bad we can't give people reputation on this board:)
Thanks!
Intern
Joined: 17 Nov 2006
Posts: 19
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: DS - board of directors [#permalink]  10 Dec 2006, 16:57
arjsingh1976 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%

Is the answer 40% ? I am getting 20%. Well from what i understand it is

(No. Subcommittess including both Michael and Anthony) / (No. of all possible Subcommittees)

Which is 4C1 / 6C3 = 4/20 = 20%

What you guys are talking about is No. of subcommitees which has Michael, and not all possible subcommitees. So that number is 10

and that way u get 40%.

Senior Manager
Joined: 20 Feb 2006
Posts: 373
Followers: 1

Kudos [?]: 7 [0], given: 0

Re: DS - board of directors [#permalink]  10 Dec 2006, 17:06
arjsingh1976 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?

subcomittees that include Michael+Anthony/no. with Michael + 2 others

Last edited by MBAlad on 10 Dec 2006, 17:25, edited 1 time in total.
Manager
Joined: 10 Jul 2006
Posts: 75
Followers: 1

Kudos [?]: 2 [0], given: 0

Re: DS - board of directors [#permalink]  10 Dec 2006, 17:15
das_go wrote:
arjsingh1976 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%

Is the answer 40% ? I am getting 20%. Well from what i understand it is

(No. Subcommittess including both Michael and Anthony) / (No. of all possible Subcommittees)

Which is 4C1 / 6C3 = 4/20 = 20%

What you guys are talking about is No. of subcommitees which has Michael, and not all possible subcommitees. So that number is 10

and that way u get 40%.

I solved this problem the same way as you did. However, I think the number of all possible subcommittees would be 10 instead of 20. (6C3)/2.
You are correct on the number of all possible sub committee if out of 6, you only have to pick 3 people. However, when the 6 people are SPLIT into 2 subgroupd, then when you pick out the 3 people, the other 3 left would also set one arrangement. so to avoid double counting, we need to divide that amount by 2. So, 20/2 = 10. the rest is the same.

Hope that makes sense.
Senior Manager
Joined: 20 Feb 2006
Posts: 373
Followers: 1

Kudos [?]: 7 [0], given: 0

All possible with Michael = 5C2 = 5*4/2*1 = 10

As you've said, by selecting one individual subcommittee you leave a corresponding unique subcommittee so total number of unique subcommittees = 10

Note: We use 5C2 (not 6C3) because we are looking at total number of subcommittees with Michael, not the total number possible. Therefore, Michael has already taken the first seat so we look at the number of ways to choose two people from the remaining 5.
Similar topics Replies Last post
Similar
Topics:
1 How many computers did Michael, a salesman for the computer 1 01 Nov 2012, 01:12
Michael's broker sends Michael a margin call if the equity 3 25 Oct 2012, 19:18
On January, 1, 2002, Michael invested a certain amount of 3 18 Feb 2011, 10:56
DS question (Directors and managers) 1 26 Aug 2007, 06:33
DS: directors managers: GMATprep 3 17 Jul 2006, 12:38
Display posts from previous: Sort by