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>r!</math> (the [[factorial]] of r) permutations of a set with r objects. | + | 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. |
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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 (n-1) objects we can choose, (n-2) for the third, and so on. In general, the number of ways to permute r objects from a set of n is given by | ||
| + | <math>P(n,r)=n(n-1)(n-2)\cdots(n-r+1)=\frac{n!}{(n-r)!}</math>. | ||
Revision as of 12:09, 29 June 2006
A permutation of a set of r objects is any rearrangement of the r objects. There are 
(the factorial of r) permutations of a set with r objects.
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 (n-1) objects we can choose, (n-2) for the third, and so on. In general, the number of ways to permute r objects from a set of n is given by
.
