Combinations, arrangements and permutations calculator

Calculate combinations C(n,r), arrangements P(n,r) and the factorial from n and r.

Combination C(n,r) — no order

50,063,860

Arrangement P(n,r) — ordered36,045,979,200

Factorial of n (n!)8.3210e+81

Use combination when order does not matter (e.g. lottery) and arrangement when it does (e.g. podium).

How the calculation works

Combination (order ignored): C(n,r) = n! / (r!·(n−r)!). Arrangement (order matters): P(n,r) = n! / (n−r)!.

How many combinations of 6 from 60?

C(60,6) = 50,063,860 possible combinations.

Paste a list of numbers and get mean, median, standard deviation, min, max and sum.

Add, subtract, multiply and divide fractions, with the result already simplified.

Updated on June 18, 2026 · by Rafael Rossi · Methodology & sources