数学

Permutation & Combination Calculator

Calculate combinations (nCr) and permutations (nPr) to find how many ways you can choose items from a set.

Must be less than or equal to n (for without replacement).

Combinations (nCr)

Order does NOT matter (e.g. hand of cards)

Without replacement —
With replacement —

Permutations (nPr)

Order DOES matter (e.g. combination lock)

Without replacement —
With replacement —
使い方
  1. Enter n: the total number of objects you have to choose from.
  2. Enter r: the number of objects you are selecting.
  3. The calculator determines the total possible ways to select them, distinguishing between combinations (where order doesn't matter) and permutations (where order matters).

計算式

Combinations (No Replacement):
nCr = n! / [r! × (n - r)!]

Permutations (No Replacement):
nPr = n! / (n - r)!

Combinations (With Replacement):
CR = (n + r - 1)! / [r! × (n - 1)!]

Permutations (With Replacement):
PR = nr

A Permutation and Combination Calculator solves complex combinatorics problems in seconds. "Combinations" are used when the order of selection doesn't matter (like choosing 5 players from a team of 10). "Permutations" are used when the sequence is strictly enforced (like guessing a 4-digit PIN code).