Permutation Calculator

Calculate the number of permutations (nPr) for selecting r objects from n distinct objects where order matters

Calculate Permutations

The total number of distinct objects in the set

The number of objects to choose from the set

Results

Permutations
0
P(0,0) = 0! / (0-0)!

Example Calculation

Card Number Example

Problem: You have 9 cards numbered 1 to 9. How many distinct 3-digit numbers can you create?

Solution: This is a permutation problem where n=9 and r=3

Formula: P(9,3) = 9! / (9-3)! = 9! / 6!

Calculation: P(9,3) = 9 × 8 × 7 = 504

Answer: 504 distinct 3-digit numbers

Key Concepts

P

Permutation

Order matters

ABC ≠ BAC

C

Combination

Order doesn't matter

ABC = BAC

!

Factorial

n! = n × (n-1) × ... × 1

5! = 5 × 4 × 3 × 2 × 1 = 120

Formula Reference

P(n,r) = n! / (n-r)!
Permutations
C(n,r) = n! / (r!(n-r)!)
Combinations

n: Total number of objects

r: Number of objects to select

Constraint: 0 ≤ r ≤ n

Understanding Permutations

What are Permutations?

A permutation is the number of ways to choose r elements from a set of n distinct objects where the order of selection matters. In other words, different arrangements of the same elements are counted as different permutations.

When to Use Permutations?

  • Password creation with specific positions
  • Race finishing positions
  • Seating arrangements
  • Creating numbers from digits

Formula Breakdown

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

P(n,r): Number of permutations

n: Total number of distinct objects

r: Number of objects to select

n!: Factorial of n

(n-r)!: Factorial of (n-r)

Special Cases:
• P(n,0) = 1 (one way to select nothing)
• P(n,n) = n! (all possible arrangements)

Permutations vs Combinations

Permutations (Order Matters)

Different arrangements of the same elements are counted separately.

Example: ABC, ACB, BAC, BCA, CAB, CBA are all different

Combinations (Order Doesn't Matter)

Different arrangements of the same elements are counted as one.

Example: ABC, ACB, BAC, BCA, CAB, CBA count as one combination