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# How many different subcommittees can be formed among the six members

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Math Expert
Joined: 02 Sep 2009
Posts: 55188
How many different subcommittees can be formed among the six members  [#permalink]

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31 Jan 2017, 10:10
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:56) correct 25% (00:55) wrong based on 287 sessions

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How many different subcommittees can be formed among the six members of the housing committee?

(1) All subcommittees must have at least two members.
(2) Any combination of members is acceptable except those with 1 member.

_________________
Intern
Joined: 18 Oct 2016
Posts: 4
Location: Italy
Concentration: Economics, Finance
GMAT 1: 550 Q42 V24
GPA: 3.5
Re: How many different subcommittees can be formed among the six members  [#permalink]

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31 Jan 2017, 10:32
2
Statements 1 and 2 give the same information, hence the possible answers are D or E.

Let's use complement strategy: P(A)= 1 - P(NOT A).

Wrong possibilities--> subcommitties with only 1 member--> 6 members--> 6 possible subcommitties.

Total possible subcommitties: 6! = 720.

P(A) = 720 - 6 = 714.

Intern
Joined: 17 Apr 2017
Posts: 7
Re: How many different subcommittees can be formed among the six members  [#permalink]

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23 Apr 2017, 05:42
1
Total number of ways of forming :

3 committees of 2 members each = 6C2 x 4C2 = 90
2 committees of 3 members each = 6C3 = 20
2 committees of 4 and 2 members = 6C4 = 15

Total number of ways = 125
Senior Manager
Joined: 17 Mar 2014
Posts: 431
Re: How many different subcommittees can be formed among the six members  [#permalink]

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09 Jan 2019, 13:00
pigi512 wrote:
Statements 1 and 2 give the same information, hence the possible answers are D or E.

Let's use complement strategy: P(A)= 1 - P(NOT A).

Wrong possibilities--> subcommitties with only 1 member--> 6 members--> 6 possible subcommitties.

Total possible subcommitties: 6! = 720.

P(A) = 720 - 6 = 714.

Bunuel,

Is above method correct ?

Thanks
Re: How many different subcommittees can be formed among the six members   [#permalink] 09 Jan 2019, 13:00
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