Probability Calculator

The Probability Calculator is a powerful tool for calculating permutations, combinations, and factorials. These mathematical concepts are essential in statistics, combinatorics, and probability theory. Use this tool to quickly solve problems involving arranging and selecting items.

Permutations (nPr) count the ways to arrange items where order matters. For example, arranging 3 people in a row: ABC, ACB, BAC, BCA, CAB, CBA = 6 permutations.

Combinations (nCr) count the ways to select items where order does not matter. For example, choosing 2 out of 3 people: AB, AC, BC = 3 combinations.

A factorial (n!) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow very fast — 10! = 3,628,800. This tool can compute factorials up to 1000!.

To calculate a permutation, enter the total number of items (n) and the number to arrange (r). The formula is nPr = n!/(n−r)!. For example, choosing a chair, vice chair, and secretary from 10 people: 10P3 = 720 different ways.

To calculate a combination, enter the total number of items (n) and the number to select (r). The formula is nCr = n!/((n−r)! × r!). For example, choosing 3 winners from 10 participants: 10C3 = 120 different combinations.

Lottery odds: if you must match 6 numbers out of 49, use 49C6 = 13,983,816 combinations.

PIN permutations: a 4-digit PIN using digits 0–9 has 10P4 = 5,040 possible arrangements.

Team selection: choosing 5 starters from 12 players gives 12C5 = 792 possible teams.