Permutation & Combination Calculator
Calculate nPr (ordered arrangements) and nCr (unordered selections) with factorials, for probability and combinatorics.
Combinations nCr
120
Breakdown
- Permutations nPr
- 720
- n! (n factorial)
- 3,628,800
- Validation
- Valid (r ≤ n)
Last updated:
FAQ
What is the difference between nPr and nCr?
nPr counts ordered arrangements (ABC ≠ BAC); nCr counts unordered selections (ABC = BAC). nPr = nCr × r!.
How many ways can I choose 3 pizzas from 10 toppings?
Order does not matter, so it is a combination: 10C3 = 120. If order mattered (like a ranked top-3), it would be 10P3 = 720.
What is 0 factorial?
By definition 0! = 1 (the empty product). This keeps formulas like nC0 = 1 mathematically consistent.
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