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
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
Permutation
Order matters
ABC ≠ BAC
Combination
Order doesn't matter
ABC = BAC
Factorial
n! = n × (n-1) × ... × 1
5! = 5 × 4 × 3 × 2 × 1 = 120
Formula Reference
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