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The University of Maryland, University of Vermont, and Emory

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The University of Maryland, University of Vermont, and Emory [#permalink] New post 14 May 2019, 00:39
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The University of Maryland, University of Vermont, and Emory University hav e each 4 soccer players. If a team of 9 is to be formed with an equal number of players from each university, how many number of ways can the selections be done?

(A) 3

(B) 4

(C) 12

(D) 16

(E) 25
[Reveal] Spoiler: OA

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Re: The University of Maryland, University of Vermont, and Emory [#permalink] New post 15 May 2019, 05:43
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The University of Maryland, University of Vermont, and Emory University have each 4 soccer players. If a team of 9 is to be formed with an equal number of players from each university, how many number of ways can the selections be done?

To avoid using Combination or Permutation notation, think through the problem logically.

If a team of nine is to be formed with an equal number of players from three teams, then each team must contribute 3 players. Since there are 4 players available from each team that means that in each combination only one player will be left out, which implies that at any given time one of the 4 players could be left out. Therefore, there are logically only 4 ways to select the playing players from each team.

Then, since there are 4 available combinations from each team and three teams in total, add those three outcomes together to find that there are 4 + 4 + 4 = 12 different combinations of available players, which matches choice C.
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Re: The University of Maryland, University of Vermont, and Emory [#permalink] New post 22 Aug 2019, 18:21
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Carcass wrote:
The University of Maryland, University of Vermont, and Emory University hav e each 4 soccer players. If a team of 9 is to be formed with an equal number of players from each university, how many number of ways can the selections be done?

(A) 3

(B) 4

(C) 12

(D) 16

(E) 25


We have 4 people and we're choosing 3. We're doing that 3 times.
4c3*3 = 12

Answer is C.
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Re: The University of Maryland, University of Vermont, and Emory [#permalink] New post 27 Aug 2019, 13:40
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MyGuruStefan wrote:
Quote:
The University of Maryland, University of Vermont, and Emory University have each 4 soccer players. If a team of 9 is to be formed with an equal number of players from each university, how many number of ways can the selections be done?

To avoid using Combination or Permutation notation, think through the problem logically.

If a team of nine is to be formed with an equal number of players from three teams, then each team must contribute 3 players. Since there are 4 players available from each team that means that in each combination only one player will be left out, which implies that at any given time one of the 4 players could be left out. Therefore, there are logically only 4 ways to select the playing players from each team.

Then, since there are 4 available combinations from each team and three teams in total, add those three outcomes together to find that there are 4 + 4 + 4 = 12 different combinations of available players, which matches choice C.


Are we looking for the number of ways to arrange the 9-player team? If so, doesn't the Fundamental Counting Principle tell us to MULTIPLY the number of ways each individual team can make the selection? In this case, I think the answer should be 4*4*4 = 64
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Re: The University of Maryland, University of Vermont, and Emory [#permalink] New post 16 Nov 2019, 21:00
64???
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Re: The University of Maryland, University of Vermont, and Emory [#permalink] New post 17 Nov 2019, 09:23
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170896 wrote:
Are we looking for the number of ways to arrange the 9-player team? If so, doesn't the Fundamental Counting Principle tell us to MULTIPLY the number of ways each individual team can make the selection? In this case, I think the answer should be 4*4*4 = 64

That would be the method for finding a THREE player team, not a nine-player team :-)
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Re: The University of Maryland, University of Vermont, and Emory [#permalink] New post 29 Nov 2019, 02:43
What will be the answer if the question like this ------

The University of Maryland, University of Vermont, and Emory University have each 4 soccer players. If a team of 9 is to be formed with an equal number of players from each university, how many possible teams are there?
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Re: The University of Maryland, University of Vermont, and Emory   [#permalink] 29 Nov 2019, 02:43
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