Combinations & Permutations

Calculate nCr and nPr with a visual showing selected vs. total arrangements

C(10,3) = 10! / (3! × 7!) = 120

Combinations C(n,r) C(10,3)

120

Permutations P(n,r) P(10,3)

720

C = 10! / (3! × 7!)

P = 10! / 7!

About this calculator

The Combinations and Permutations Calculator computes C(n,r) and P(n,r) for any n and r, showing both formulas and results side by side. Combinations count selections where order doesn't matter; permutations count arrangements where order does matter. Ideal for probability, statistics, and combinatorics problems.

Common examples

C(10, 3) = 120 combinations (choosing 3 from 10, order doesn't matter)
P(10, 3) = 720 permutations (arranging 3 from 10, order matters)
C(52, 5) = 2,598,960 — 5-card poker hand combinations
P(5, 5) = 120 — ways to arrange 5 people in 5 seats
C(6, 2) = 15 combinations vs P(6, 2) = 30 permutations