Skip to content

Combinations & permutations calculator

How many ways to choose r items from n: combinations (order doesn’t matter), permutations (order matters), with or without repeats.

Favorite

Results

Combinations C(n, r) 2,598,960

How it works

C(n, r) = n! ÷ (r! (n − r)!) · P(n, r) = n! ÷ (n − r)!

If order matters (a race podium, a PIN), count permutations: n choices for the first spot, n − 1 for the next and so on. If order doesn’t matter (a lottery ticket, a hand of cards), divide by the r! ways of arranging the same picks: that’s combinations. A 5-card poker hand from 52 cards has C(52, 5) = 2,598,960 possibilities.

  1. P(n, r) = n × (n − 1) × … × (n − r + 1) P(52, 5) = 311,875,200
  2. C(n, r) = P(n, r) ÷ r! 311,875,200 ÷ 5! = 2,598,960

Printed from rocketcalc.io/math/combinations