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# A committee is composed of a president, a vice president, and a

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Math Expert
Joined: 02 Sep 2009
Posts: 54375
A committee is composed of a president, a vice president, and a  [#permalink]

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17 Aug 2017, 01:08
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Difficulty:

15% (low)

Question Stats:

79% (00:44) correct 21% (00:37) wrong based on 108 sessions

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A committee is composed of a president, a vice president, and a treasurer. If six people are trying out for the three positions, how many different committees result?

(A) 20
(B) 40
(C) 60
(D) 105
(E) 120

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A committee is composed of a president, a vice president, and a  [#permalink]

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Updated on: 17 Aug 2017, 02:51
Bunuel wrote:
A committee is composed of a president, a vice president, and a treasurer. If six people are trying out for the three positions, how many different committees result?

(A) 20
(B) 40
(C) 60
(D) 105
(E) 120

first position = 6 options
second position = 5 options
third position = 4 options

6*5*4= 120
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Originally posted by Luckisnoexcuse on 17 Aug 2017, 02:34.
Last edited by Luckisnoexcuse on 17 Aug 2017, 02:51, edited 1 time in total.
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Re: A committee is composed of a president, a vice president, and a  [#permalink]

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17 Aug 2017, 02:43
Here order is important..so 6p3 =120

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Re: A committee is composed of a president, a vice president, and a  [#permalink]

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17 Aug 2017, 02:53
Bunuel wrote:
A committee is composed of a president, a vice president, and a treasurer. If six people are trying out for the three positions, how many different committees result?

(A) 20
(B) 40
(C) 60
(D) 105
(E) 120

6*5*4 = 120

ALTERNATIVE
6C3*3! = 20*6 = 120

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Re: A committee is composed of a president, a vice president, and a  [#permalink]

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24 Aug 2017, 13:42
Bunuel wrote:
A committee is composed of a president, a vice president, and a treasurer. If six people are trying out for the three positions, how many different committees result?

(A) 20
(B) 40
(C) 60
(D) 105
(E) 120

Since we have specific positions on the committee, order matters and we have a permutation. Thus, the number of ways to select 3 people from 6 is 6P3 = 6!/3! = 6 x 5 x 4 = 120.

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Re: A committee is composed of a president, a vice president, and a   [#permalink] 24 Aug 2017, 13:42
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# A committee is composed of a president, a vice president, and a

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