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# 4 baseball players each stand at different corners of a base

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4 baseball players each stand at different corners of a base [#permalink]

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08 Aug 2013, 12:17
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Question Stats:

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4 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?

A. 4
B. 6
C. 16
D. 24
E. 256
[Reveal] Spoiler: OA

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Re: 4 baseball players each stand at different corners of a base [#permalink]

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08 Aug 2013, 12:19
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gmatpapa wrote:
4 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?

A. 4
B. 6
C. 16
D. 24
E. 256

it is like a circular arrangement.

total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 4
hence ans = 3 factorial = 6

hence B
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Re: 4 baseball players each stand at different corners of a base [#permalink]

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08 Aug 2013, 12:45
gmatpapa wrote:
4 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?

A. 4
B. 6
C. 16
D. 24
E. 256

....................
for circular permutation, just minus 1 and permute.
so 3! = 6 ways
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Re: 4 baseball players each stand at different corners of a base [#permalink]

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24 Dec 2014, 12:21
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Re: 4 baseball players each stand at different corners of a base [#permalink]

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24 Dec 2014, 15:57
Expert's post
Hi All,

These types of permutation questions can sometimes be confusing, so you might find that a "visual component" will help you to stay organized and get to the correct answer.

In this question, we have to place 4 players at 4 corners of a diamond (although you could just as easily have a question that places them at equidistant spots on a circle).

If we were placing those 4 players in a straight line, then the number of possibilities would be a simple calculation:

(4)(3)(2)(1) = 24

HOWEVER, since we're told that we can count an option ONLY if the relative positions of the players differ.

This means that the following 4 options are all the SAME thing:
ABCD
BCDA
CDAB
DABC

The first option (ABCD) is simply "revolved" around the diamond, so the relative positions of the players are NOT different.

Mathematically, we have to divide 24 by 4, so that remove all of the "duplicates"

[Reveal] Spoiler:
B

All in all, this a relatively rare issue on the GMAT (you probably won't see it; even if you aced the Quant section, you still probably wouldn't see it).

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# 4 baseball players each stand at different corners of a base

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