MultiConvers

Permutation and Combination Calculator

Enter n and r as whole numbers. Use permutations when the order of the selection matters, combinations when it does not.

How it works

A permutation is an ordered selection: P(n, r) = n! / (n−r)!. A combination is an unordered selection: C(n, r) = n! / (r!(n−r)!). P(5, 2) = 5×4 = 20 (first and second place).

C(5, 2) = 10 (a pair from five people). n and r must be integers, r cannot exceed n, and neither can be negative. Overflow is rejected instead of Infinity.

Formula

P(n, r) = n! / (n − r)!
C(n, r) = n! / (r! (n − r)!)

Worked examples

  • Permutations of 5 take 2

    P(5, 2) → 20

  • Combinations of 5 take 2

    C(5, 2) → 10

Useful notes

  • C(n, 0) = 1 and P(n, 0) = 1: there is one way to choose nothing.

FAQ

When do I use permutations vs combinations?

Permutations if order matters (gold/silver, a PIN). Combinations if it does not (a committee, a dealt hand).

Why is C(5, 2) smaller than P(5, 2)?

Each pair of people can be lined up in 2! = 2 ways. Dividing by r! removes that extra order.

What if r is larger than n?

You cannot choose more items than you have. The result is rejected.

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