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Permutation (nPr) Calculator

Permutation (nPr) Calculator


What are permutations?

Permutations are the number of different combinations in different orders that can be made from a group of items.
For example, the numbers 1, 2, and 3 have the following 6 different 2 number permutations:
1 2
1 3
2 1
2 3
3 1
3 3
The numbers 1, 2, 3, and 4 have the following 12 different 2 number permutations:
1 2
1 3
1 4
2 1
2 3
2 4
3 1
3 2
3 4
4 1
4 2
4 3
The numbers 1, 2, 3, and 4 have the following 24 different 3 number permutations:
1 2 3
1 2 4
1 3 2
1 3 4
1 4 2
1 4 3
2 1 3
2 1 4
2 3 1
2 3 4
2 4 1
2 4 3
3 1 2
3 1 4
3 2 1
3 2 4
3 4 1
3 4 2
4 1 2
4 1 3
4 2 1
4 2 3
4 3 1
4 3 2

How are permutations calculated?

Permutations are calculated by the formula:
frac{text{number of items}!}{(text{number of items} - text{items in each permutation})! times text{items in each permutation}!}

Example

How many different permutations of 3 can be made from 10 different items?
frac{10!}{(10 - 3)! times 3!}
frac{3628800}{5040 times 6}
frac{3,628,800}{30,240}
120

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