How to calculate permutations
C(n,r) = n! ÷ (r!(n−r)!); P(n,r) = n! ÷ (n−r)!
Worked example. Combinations (order doesn't matter): 120.
Example inputs — Total items (n): 10; Chosen at a time (r): 3. Starting values are illustrative.
From George Guju, founder of Calculyn · Educational calculator guidance, not professional advice.
How it works
Combinations count groups where order is irrelevant (a committee); permutations count arrangements where order matters (a podium finish). Permutations are always r! times larger.
Assumptions & limitations
- Results are rounded for display.
Formula and assumptions reviewed October 2026 by the Calculyn team. How we build our calculators
Frequently asked questions
Which one for lottery odds?
Combinations — the order numbers are drawn doesn't matter.
What about repeats allowed?
With repetition, arrangements are n^r and combinations are C(n+r−1, r).