Combination and Permutation Calculator
Find nCr and nPr with the formula shown.
What is a combination and permutation calculator?
A combination and permutation calculator finds nCr and nPr: how many ways you can choose r items from n items, and how many ways you can arrange them.
How to use the combination and permutation calculator
Enter n, the total number of items, and r, how many you choose, then click Calculate. The calculator shows both nCr and nPr with the working.
Combination and permutation formulas
nCr = n! ÷ (r! × (n−r)!) and nPr = n! ÷ (n−r)!. The difference is order: order matters in a permutation, but not in a combination.
Example
For n = 5 and r = 2: nCr = 5! ÷ (2! × 3!) = 10, and nPr = 5! ÷ 3! = 20.
Frequently Asked Questions
What is nCr(5,2)?
nCr(5,2) = 10. Try it on the calculator above.
What is nPr(5,2)?
nPr(5,2) = 20. Try it on the calculator above.
What is the difference between a combination and a permutation?
In a permutation the order matters, so 20 arrangements are possible for n = 5, r = 2. In a combination the order does not matter, so there are only 10 ways to choose 2 items from 5.
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