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If a 3-member subcommittee is to be formed from a certain 6-

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If a 3-member subcommittee is to be formed from a certain 6-  [#permalink]

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New post Updated on: 01 Apr 2014, 04:57
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If a 3-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?

A. 6
B. 18
C. 20
D. 108
E. 216

Originally posted by goodyear2013 on 01 Apr 2014, 03:37.
Last edited by Bunuel on 01 Apr 2014, 04:57, edited 1 time in total.
Edited the question.
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Re: if a 3-member subcommittee is to be formed from a certain 6-  [#permalink]

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New post 01 Apr 2014, 04:56
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Re: If a 3-member subcommittee is to be formed from a certain 6-  [#permalink]

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New post 01 Apr 2014, 12:16
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goodyear2013 wrote:
If a 3-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?

A. 6
B. 18
C. 20
D. 108
E. 216

Another way:
1st member can be selected in 6 ways
2nd can be selected in 5 ways
3rd can be selected in 4 ways
So total ways : 120
But to avoid the similar scenarios 120/3!=20
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Re: If a 3-member subcommittee is to be formed from a certain 6-  [#permalink]

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New post 22 Mar 2017, 07:40
goodyear2013 wrote:
If a 3-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?

A. 6
B. 18
C. 20
D. 108
E. 216


\(6C_3 = 20\)

Thus, the answer must be (C) 20
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Re: If a 3-member subcommittee is to be formed from a certain 6-  [#permalink]

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New post 01 May 2018, 10:00
goodyear2013 wrote:
If a 3-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?

A. 6
B. 18
C. 20
D. 108
E. 216


The number of possible subcommittees is 6C3 = (6 x 5 x 4)/3! = 20.

Answer: C
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Re: If a 3-member subcommittee is to be formed from a certain 6-  [#permalink]

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New post 25 Aug 2018, 05:43
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Bunuel wrote:
goodyear2013 wrote:
if a 3-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?

A) 6
B) 18
C) 20
D) 108
E) 216


Choosing 3 out of 6: \(C^3_6=\frac{6!}{(6-3)!3!}=20\).

Answer: C.


Hi Bunuel,

Because when a 3 member committee is formed from a 6 member committee automatically two3 member committee are formed. Also, doing this way we would double count the 3 member committees in such a scenario. So should the answer be \(\frac{6C3*3C3}{2!}=10\).

Could you please help me with this fundamental query.
Thanks in advance! :-)
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Re: If a 3-member subcommittee is to be formed from a certain 6-   [#permalink] 25 Aug 2018, 05:43
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