What Is the Permutation and Combination Calculator?
A combinatorics calculator determining the exact number of possible selections and arrangements from a set.
How Does the Permutation and Combination Calculator Work?
Evaluates factorial quotients following discrete probability rules.
Permutation and Combination Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
nPr = n! / (n − r)! | nCr = n! / [r! × (n − r)!]
Factorial counting equations for ordered and unordered subsets from a population of size n.
How to Use the Permutation and Combination Calculator
- Input the total set size n, sample size r, and choose between permutation or combination.
Step-by-Step Example Calculation
Choose 3 from 8 items
Input Values:
n:8
r:3
mode:combination
Worked Steps: Yields 56 combinations and 336 ordered permutations.
Understanding Your Result
Displays the primary count alongside comparisons for repetition variants.
Factors That Affect the Result
- Set size n and subset size r.
When Should You Use This Calculator?
- Evaluating lottery probabilities, poker hand combinations, password security entropy, and experimental groupings.
Assumptions & Limitations
- All n items are distinct; integer values only.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Evaluated with exact integer arithmetic up to 64-bit bounds.