Permutation and Combination Calculator: Count Arrangements
Calculate permutations and combinations with this easy mathematical calculator.
Permutation and Combination Calculator
Understanding permutations and combinations is essential for probability, statistics, and many real-world applications. Whether you're planning a lottery strategy, organizing events, or solving mathematical problems, these concepts help you count possibilities.
Permutations (Order Matters)
A permutation counts the number of ways to arrange items where order matters.
P(n,r) = n! / (n-r)!
Example: How many ways can you arrange 3 books from a collection of 5?
P(5,3) = 5! / 2! = 60 ways
Combinations (Order Doesn't Matter)
A combination counts the number of ways to select items where order doesn't matter.
C(n,r) = n! / (r! × (n-r)!)
Example: How many ways can you choose 3 books from 5?
C(5,3) = 5! / (3! × 2!) = 10 ways
Key Difference
The fundamental difference is that permutations care about order while combinations don't. Arranging 3 books ABC is different from BAC in permutations, but they count as the same in combinations.
Real-World Applications
Lottery: Calculating odds of winning based on number selection.
Password Security: Estimating password strength based on character combinations.
Team Formation: Determining possible team compositions.
Scheduling: Calculating possible meeting arrangements.