Permutations & Combinations

Count ordered arrangements (nPr) and unordered selections (nCr) of r items from n. Essential for probability, lottery odds and combinatorics.

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nPr: 720 · nCr: 120

Worked on the example above, step by step — follow along and you can do it on paper next time, no tool required.

Permutations count ordered picks (order matters); combinations count unordered picks (order doesn't).
nPr = n! ÷ (n − r)!, which is just r terms counting down from n
10! ÷ (10 − 3)! = 720
nCr = nPr ÷ r! (divide out the orderings)
720 ÷ 3! = 120

What's the difference between nPr and nCr?

nPr counts arrangements where order matters; nCr counts selections where it doesn't.

For n=10, r=3?

720 permutations and 120 combinations.