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What is the difference between a combination and a permutation?

Guest Feb 22, 2017
 #1
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Permutation: A set of objects in which position (or order) is
important=nPr=68P5=1,250,895,360


Combination: A set of objects in which position (or order) is NOT
important.=nCr=68C5=10,424,128

Guest Feb 22, 2017
 #2
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Put simply,a combination is just a collection of objects and  permutations are different ways of arranging that combination.To show this ---

I can have a combination of 4 people on a commitee,say Art, Bert,Chas and Dave.

I could have picked this same commitee in 24 different ways ( that is 24 permutations)

To show a few,so you get the idea,I could have picked

Art,Chas,Bert,Dave or

Art,Chas,Dave,Bert or

Chas,Dave,Bert,Art     (I'm not listing all 24 of them!)      ,all of which gives me the same combination,but just permuted in different ways.

If I have a combination of 4 objects,the number of permutations of that combination is 24. Why?

-the number of choices I have for my first pick is   4.  Now I only have  3 choices left for my next pick,and at this stage ,with every one of my 4 picks,I have a choice of 3 picks  ie  4 x 3. After my 3rd pick,I only have 2 choices left, so now I have 4x3x2 permutations and finally only one left, we usually include the 1   to write 4x3x2x1.

Guest Feb 22, 2017

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