Permutation Calculator

Calculate the number of possible arrangements of r items from a set of n items.

Calculator

Enter Your Values

Total number of items in the set

Number of items to arrange

Concept

Permutation Formula

A permutation is an arrangement of objects in a specific order. The number of permutations of r items from a set of n items is given by:

Formula:
P(n,r) = n! / (n-r)!

Where:

  • n is the total number of items
  • r is the number of items to arrange
  • ! represents factorial
Steps

How to Calculate Permutations

To calculate permutations, follow these steps:

  1. 1
    Identify the total number of items (n)
  2. 2
    Determine how many items to arrange (r)
  3. 3
    Calculate n! (factorial of n)
  4. 4
    Calculate (n-r)! (factorial of n-r)
  5. 5
    Divide n! by (n-r)! to get the number of permutations
Guide

Understanding Permutations

Key points about permutations:

  • 1
    Order Matters:

    In permutations, the order of arrangement is important.

  • 2
    No Repetition:

    Each item can only be used once in the arrangement.

  • 3
    Factorial Growth:

    The number of permutations grows very quickly with n and r.

Examples

Practical Examples

Example 1 Race Positions

n = 5 runners
r = 3 positions (1st, 2nd, 3rd)

P(5,3) = 60

There are 60 possible ways to arrange 3 runners from 5.

Example 2 Password Creation

n = 10 digits (0-9)
r = 4 positions

P(10,4) = 5,040

There are 5,040 possible 4-digit passwords without repetition.

Example 3 Committee Selection

n = 8 people
r = 3 positions (President, Vice-President, Secretary)

P(8,3) = 336

There are 336 possible ways to fill these 3 positions.

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