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Permutations and Combinations

Date: 03/11/98 at 16:06:18
From: Andrew Demers
Subject: Permutations and Combinations - What's the Difference?

I am a student at Hershey Middle School. Recently I was working with 
my math teacher on combinations and permutations. He admitted that 
it was not a strong point of his and e were both wondering what the 
difference is between the two things. 

Thanks in advance.

Andrew Demers

Date: 03/12/98 at 15:33:01
From: Doctor Daniel
Subject: Re: Permutations and Combinations - What's the Difference?

Hi there,

Good question!  The difference concerns whether the order of the 
objects matters, more or less. In a permutation, the order does 
matter, while in a combination, all that matters is which set of 
objects was chosen.

Here's an example: Suppose you have eight objects, labeled A through 
H. Then the number of permutations of 5 of these eight objects is 
8x7x6x5x4; there are eight possibilities for the first, seven for the 
second, and so on. And the permutation ACHED is different from HEADC. 

For combinations, there are far fewer; here we're really asking how 
many subsets of 5 objects of the original eight there are. It 
shouldn't be too hard to convince yourself that there are 120 times 
fewer combinations than permutations. Why?  Well, consider that ALL 
permutations that include the letters FACDE are really part of the 
same combination, {A,C,D,E,F}. And there are 120 = 5! = 5x4x3x2x1 of 

Here are another couple of tidbits: The number of combinations of K 
objects chosen from a set of N is equal to N!/K!(N-K)!, while the 
number of permutations is just N!/(N-K)!  Also, why is it that there 
are exactly the same number of combinations of 5 letters out of 8 as 
there are of 3 letters out of 8 (don't just say "the formula tells me 

-Doctor Daniel,  The Math Forum
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Associated Topics:
High School Permutations and Combinations

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