What is the difference between permutations and combinations?

In permutations, order matters — selecting A then B is a different arrangement from B then A. In combinations, order does not matter, so {A,B} and {B,A} are the same group. Use permutations when sequence is significant (e.g., ranking, passwords) and combinations when it is not (e.g., lottery draws, committees).

What is P(n,r) when r equals n?

When r = n, P(n,n) = n! / 0! = n! / 1 = n!. This is the total number of ways to arrange all n items, for example the number of distinct orderings of a deck of cards (52!).

P(n,0) = n! / n! = 1. There is exactly one way to choose and arrange zero items — do nothing. This is consistent with the convention that 0! = 1.

Why does the calculator limit n to 170?

JavaScript's floating-point number (IEEE 754 double) can represent integers exactly only up to about 2^53. Factorials grow extremely fast: 171! exceeds JavaScript's maximum safe integer, so results beyond n=170 would be inaccurate. For very large n, use a big-integer math library.

Can r be larger than n?

No. You cannot arrange more items than exist in the set, so r must satisfy 0 ≤ r ≤ n. The calculator shows an error if you enter r > n.

Is P(n,r) the same as nPr?

Yes. The notations P(n,r), nPr, and P_{n,r} all mean the same thing: the number of permutations of r items taken from n.

Permutation Calculator

Name: Permutation Calculator
Availability: InStock
Author: Nham Vu

Enter n (total items) and r (items chosen) to instantly compute P(n,r) — the number of ordered arrangements.

Enter Values

n — Total number of items

Must be a non-negative integer, max 170.

r — Items to arrange (order matters)

Must satisfy 0 ≤ r ≤ n.

Quick Examples

Result

Enter n and r, then click Calculate.

Summary