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# Permutation vs. combination vs arrangement

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Intern
Joined: 23 Jan 2009
Posts: 1
Permutation vs. combination vs arrangement  [#permalink]

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23 Jan 2009, 14:45
1
can someone please give me an example repeated with slight changes that would illustrate the following?
1-a case when arrangement is used
2- a case when permutation is used
3- a case when combination is used.

I'm just having trouble understand when to use either when i read a problem and it's really confusing.

Thanks
Intern
Joined: 19 Jan 2009
Posts: 9
Re: Permutation vs. combination vs arrangement  [#permalink]

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27 Jan 2009, 09:27
can someone please give me an example repeated with slight changes that would illustrate the following?
1-a case when arrangement is used
2- a case when permutation is used
3- a case when combination is used.

I'm just having trouble understand when to use either when i read a problem and it's really confusing.

Thanks

Permutation means arrangement of things. The word arrangement is used, if the order of things is considered.

so 1 and 2 are same:)
Combination means selection of things. The word selection is used, when the order of things has no importance.

Suppose we have to form a number consisting of three digits using the digits 1,2,3,4, To form this number the digits have to be arranged. Different numbers will get formed depending upon the order in which we arrange the digits. This is an example of Permutation.

Now suppose that we have to make a team of 11 players out of 20 players, This is an example of combination, because the order of players in the team will not result in a change in the team. No matter in which order we list out the players the team will remain the same! For a different team to be formed at least one player will have to be changed.

hope it is clear now

Senior Manager
Joined: 15 Sep 2011
Posts: 301
Location: United States
WE: Corporate Finance (Manufacturing)
Re: Permutation vs. combination vs arrangement  [#permalink]

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23 Jun 2015, 18:29
pecas wrote:
can someone please give me an example repeated with slight changes that would illustrate the following?
1-a case when arrangement is used
2- a case when permutation is used
3- a case when combination is used.

I'm just having trouble understand when to use either when i read a problem and it's really confusing.

Thanks

Bumping this up because the first answer wasn't satisfactory, and I was studying it myself...

-Combination is the selection of a group from a number of items, or people. There is a group which is selected and a group not selected, and so the formula nCr has the number selected and number unselected dividing the total number. Order is without significance.
$$\frac{n!}{r!(n-r)!}$$

-Permutation is the arragement of a group from a number of items, or people. There is a group which is selected AND ordered, and the formula nPr has the number of unselected dividing the total number. The order of the items, or people, selected are what concerns us, and therefore the unselected is cleared out.
$$\frac{n!}{(n-r)!}$$

Tip:
-If you are working from selection and the solution is required without order, divide by the number of which are not to be ordered. That said, the reverse is true too; if you are working from an ordered solution, multiply by number of items selected to unarrage them.
-Slot method is a way of setting up a problem, and it is used for both combination and permutations, selections and arrangements, respectively.
-Arragement is what the problem is asking for, but permutation is the standard formula to solve it.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10463
Location: Pune, India
Re: Permutation vs. combination vs arrangement  [#permalink]

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23 Jun 2015, 21:16
mejia401 wrote:
-Slot method is a way of setting up a problem, and it is used for both combination and permutations, selections and arrangements, respectively.

Note here that slot method by default arranges. You are choosing for particular slots so you have numbered the positions. That is arrangement. If it is pure selection, you will have to un-arrange the result.

Check this post:
http://www.veritasprep.com/blog/2011/11 ... binations/
The basic counting principle is the same as slot method.
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Karishma
Veritas Prep GMAT Instructor

Senior Manager
Joined: 15 Sep 2011
Posts: 301
Location: United States
WE: Corporate Finance (Manufacturing)
Permutation vs. combination vs arrangement  [#permalink]

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24 Jun 2015, 11:29
VeritasPrepKarishma wrote:
mejia401 wrote:
-Slot method is a way of setting up a problem, and it is used for both combination and permutations, selections and arrangements, respectively.

Note here that slot method by default arranges. You are choosing for particular slots so you have numbered the positions. That is arrangement. If it is pure selection, you will have to un-arrange the result.

Check this post:
http://www.veritasprep.com/blog/2011/11 ... binations/
The basic counting principle is the same as slot method.

Good point, Thanks Karishma. They are all so closely related that it's awfully easy to get tied up in them and trip. Slot method, or the basic counting principle, is an arrangement first before anything else.
Permutation vs. combination vs arrangement   [#permalink] 24 Jun 2015, 11:29