Permutation & Combination Calculator

Calculate P(n,r) permutations and C(n,r) combinations with step-by-step factorial working. Includes Pascal's triangle and real-world examples.

Calculate P(n,r) and C(n,r)

n (total items) ?

r (items chosen) ?

Factorial Calculator

Results

C(10, 3) — Combinations

120

Ways to choose 3 from 10 (order doesn't matter)

P(10, 3) — Permutations

720

Ways to arrange 3 from 10 (order matters)

Property	Value

Step-by-Step Working

Pascal's Triangle (first 10 rows) — C(n,r) values

Highlighted cell shows your C(n,r) result. Each value is the sum of the two above it.

Australian Lottery Odds Reference

Lottery	Draw format	Jackpot odds (C formula)	Approx. odds
Tattslotto / Gold Lotto	6 from 45	C(45,6)	1 in 8,145,060
Oz Lotto	7 from 45	C(45,7)	1 in 45,379,620
Powerball (main)	7 from 35 + 1 from 20	C(35,7) × C(20,1)	1 in 134,490,400
Set for Life	8 from 37	C(37,8)	1 in 38,608,020

Permutations vs Combinations

Both deal with selecting r items from n items, but the key difference is whether order matters.

	Formula	Order matters?	Example
Permutation P(n,r)	n! / (n−r)!	Yes	Race results, passwords, seating arrangements
Combination C(n,r)	n! / (r! × (n−r)!)	No	Lottery picks, committees, card hands

P(n,r) = C(n,r) × r! — permutations equal combinations multiplied by all the ways r items can be arranged (r!)