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Jasper is to select a committee of 4 individuals from among a group of

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Bunuel
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Jasper is to select a committee of 4 individuals from among a group of [#permalink] New post   13 Dec 2018, 00:26
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Jasper is to select a committee of 4 individuals from among a group of 5 candi­dates. The committee will have a President, a Vice President, and two Trea­surers. How many different committees can John select from the 5 candidates?

A. 15
B. 20
C. 30
D. 60
E. 120
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D
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Jasper is to select a committee of 4 individuals from among a group of [#permalink] New post   13 Dec 2018, 02:02
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Bunuel wrote:
Jasper is to select a committee of 4 individuals from among a group of 5 candi­dates. The committee will have a President, a Vice President, and two Trea­surers. How many different committees can John select from the 5 candidates?

A. 15
B. 20
C. 30
D. 60
E. 120



two ways to solve :

method 1:
5!/ 1!*1!*2! = 60

method 2: 5c1*4c1* 3c2 = 5*4*3 = 60

IMO D
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Re: Jasper is to select a committee of 4 individuals from among a group of [#permalink] New post   19 Jan 2020, 12:12
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You have 5 choices for President, 4 choices for Vice-President, and then to pick the two Treasurers, we can just choose one of the 3 remaining people to leave off of the committee. Multiplying our choices, the answer is (5)(4)(3) = 60.
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Re: Jasper is to select a committee of 4 individuals from among a group of [#permalink] New post   23 Jan 2020, 10:11
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Bunuel wrote:
Jasper is to select a committee of 4 individuals from among a group of 5 candi­dates. The committee will have a President, a Vice President, and two Trea­surers. How many different committees can John select from the 5 candidates?

A. 15
B. 20
C. 30
D. 60
E. 120


First, the number of ways of choosing 4 people from 5 is 5C4 = 5. Next, the number of ways of arranging 1 President, 1 VP and 2 Treasurers is 4!/2! = 24/2 = 12. Therefore, the total number of ways is:

5 x 12 = 60

Answer: D
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Re: Jasper is to select a committee of 4 individuals from among a group of [#permalink] New post   19 Jan 2020, 11:21
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The question can be done in 2 steps:
1) select 4 individuals can be chosen out of 5 in 5C4 or 5C1 ways = 5 ways
2) Now we need to assign the designations: P, VP, T, T
it can be done in 4!/(2!) = 12 ways
Hence total no of ways = selection and assigning designation = 5*12 = 60

Answer D

Bunuel wrote:
Jasper is to select a committee of 4 individuals from among a group of 5 candi­dates. The committee will have a President, a Vice President, and two Trea­surers. How many different committees can John select from the 5 candidates?

A. 15
B. 20
C. 30
D. 60
E. 120
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Re: Jasper is to select a committee of 4 individuals from among a group of [#permalink] New post   21 Jan 2020, 18:56
Bunuel wrote:
Jasper is to select a committee of 4 individuals from among a group of 5 candi­dates. The committee will have a President, a Vice President, and two Trea­surers. How many different committees can John select from the 5 candidates?

A. 15
B. 20
C. 30
D. 60
E. 120




Why 5C4 is not an answer? Can someone please explain.
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Re: Jasper is to select a committee of 4 individuals from among a group of [#permalink]
21 Jan 2020, 18:56
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