Difference between revisions of "Permutation"
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| − | A '''permutation''' of a set of r objects is any rearrangement of the r objects. There are <math>\displaystyle r!</math> (the [[factorial]] of r) permutations of a set with r objects. | + | {{stub}} |
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| + | A '''permutation''' of a [[set]] of <math>r</math> objects is any rearrangement (linear ordering) of the <math>r</math> objects. There are <math>\displaystyle r!</math> (the [[factorial]] of <math>r</math>) permutations of a set with <math>r</math> objects. | ||
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| − | An important question is how many ways to pick an r-element subset of a set with n elements, where order matters. To find how many ways we can do this, note that for the first of the r elements, we have n different objects we can choose from. For the second element, there are | + | An important question is how many ways to pick an <math>r</math>-element [[subset]] of a set with <math>n</math> elements, where order matters. To find how many ways we can do this, note that for the first of the <math>r</math> elements, we have <math>n</math> different objects we can choose from. For the second element, there are <math>n-1</math> objects we can choose, <math>n-2</math> for the third, and so on. In general, the number of ways to permute <math>r</math> objects from a set of <math>n</math> is given by |
<math>P(n,r)=n(n-1)(n-2)\cdots(n-r+1)=\frac{n!}{(n-r)!}</math>. | <math>P(n,r)=n(n-1)(n-2)\cdots(n-r+1)=\frac{n!}{(n-r)!}</math>. | ||
== See also == | == See also == | ||
* [[Combinatorics]] | * [[Combinatorics]] | ||
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Revision as of 09:48, 9 August 2006
This article is a stub. Help us out by expanding it.
A permutation of a set of 
objects is any rearrangement (linear ordering) of the objects. There are 
(the factorial of ) permutations of a set with objects.
An important question is how many ways to pick an -element subset of a set with 
elements, where order matters. To find how many ways we can do this, note that for the first of the elements, we have different objects we can choose from. For the second element, there are 
objects we can choose, 
for the third, and so on. In general, the number of ways to permute objects from a set of is given by
.
