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From a group of 18 athletes that include 10 people with professional

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From a group of 18 athletes that include 10 people with professional  [#permalink]

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New post 27 Jan 2019, 10:26
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  25% (medium)

Question Stats:

74% (01:04) correct 26% (01:53) wrong based on 48 sessions

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From a group of 18 athletes that include 10 people with professional experience, a 3-person team is to be selected so that exactly 1 person on the team has professional experience. How many different teams of this type are possible?

(A) 280
(B) 360
(C) 504
(D) 560
(E) 816


Explanation:
The team we’re looking for will choose 1 person from a population of 10 with professional experience. There are 10 such choices. The team will also have 2 people from the remaining 8 who do not have professional experience. The number of such choices is determined by the combinations formula: n!/k!(n−k)! = 8!/2!(8−2)! = 8!/2!6! = 8×7/2 = 28
Since there are 10 choices for the one professional and 28 choices for the pairs of non-professionals, the total number of possible teams is the product: 28 × 10 = 280, choice (A).
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Re: From a group of 18 athletes that include 10 people with professional  [#permalink]

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New post 27 Jan 2019, 18:26
Ways of choosing 1 professional from 10 = 10C1= 10
Ways of choosing 2people from remaining 8 = 8C2 = 8*7/2*1 = 28
Total ways = 28 * 10 = 280
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Re: From a group of 18 athletes that include 10 people with professional  [#permalink]

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New post 27 Jan 2019, 21:31
energetics wrote:
From a group of 18 athletes that include 10 people with professional experience, a 3-person team is to be selected so that exactly 1 person on the team has professional experience. How many different teams of this type are possible?

(A) 280
(B) 360
(C) 504
(D) 560
(E) 816


Explanation:
The team we’re looking for will choose 1 person from a population of 10 with professional experience. There are 10 such choices. The team will also have 2 people from the remaining 8 who do not have professional experience. The number of such choices is determined by the combinations formula: n!/k!(n−k)! = 8!/2!(8−2)! = 8!/2!6! = 8×7/2 = 28
Since there are 10 choices for the one professional and 28 choices for the pairs of non-professionals, the total number of possible teams is the product: 28 × 10 = 280, choice (A).


This is a copy of the following GMAT Prep question: https://gmatclub.com/forum/from-a-group ... 36299.html
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Re: From a group of 18 athletes that include 10 people with professional   [#permalink] 27 Jan 2019, 21:31
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