Permutations Calculator (nPr)

Permutations Calculator

Calculate nPr - Order matters - Arrangements where sequence is important

PermutationsCombinations
Active Formula

Result: 5P3

60

Possible ordered arrangements of 3 items from 5

Understanding Permutations vs Combinations

The key difference is whether **order matters**. Use permutations when the sequence or arrangement is important, and combinations when you only care about which items are selected.

Permutations (nPr)
  • Order matters: ABC ≠ BAC
  • Examples: Race rankings, password sequences
  • Formula:
Combinations (nCr)
  • Order doesn't matter: ABC = BAC
  • Examples: Team selection, lottery numbers
  • Formula:

Permutations Guide Guide

How to Use

  1. 1Enter the total number of items (n).
  2. 2Enter the number of items to choose (r).
  3. 3Click Calculate to find value of P(n, r).
  4. 4Remember: In permutations, ORDER MATTERS.

Formula & Logic

A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

n= Total items in the set
r= Items taken for arrangement
!= Factorial (e.g., 5! = 5×4×3×2×1)

Practical Applications

Passwords & Security

Calculate the number of possible passwords given a specific length and character set.

Race Results

Determine the number of ways runners can finish in 1st, 2nd, and 3rd place.

Seating Arrangements

Find the number of ways specific people can be seated in a row of chairs.

Frequently Asked Questions

Q.What is the difference between Permutation and Combination?

The key difference is order. For Permutations, order matters (ABC is different from CBA). For Combinations, order does not matter (ABC is the same as CBA).

Q.What do n and r stand for?

'n' represents the total number of items to choose from, and 'r' represents how many items you are choosing and arranging.

Q.What is a factorial (!)?

A factorial implies multiplying a number by every integer below it down to 1. For example, 4! = 4 × 3 × 2 × 1 = 24.