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How many different subcommittees can be formed among the six members

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

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New post 31 Jan 2017, 10:10
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

75% (00:58) correct 25% (00:57) wrong based on 210 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.

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Re: How many different subcommittees can be formed among the six members  [#permalink]

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New post 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.

Answer D
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Re: How many different subcommittees can be formed among the six members  [#permalink]

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New post 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
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Re: How many different subcommittees can be formed among the six members  [#permalink]

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New post 02 Aug 2018, 09:47
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Re: How many different subcommittees can be formed among the six members &nbs [#permalink] 02 Aug 2018, 09:47
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