What Is the Permutation and Combination Calculator?
Permutations and combinations measure how many ways items can be selected from a group.
How Does the Permutation and Combination Calculator Work?
Permutations: n × (n-1) × … × (n-r+1). Combinations: divide permutations by r! to remove order.
Permutation and Combination Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Permutations count ordered arrangements; combinations count unordered subsets.
How to Use the Permutation and Combination Calculator
- Enter n (total) and r (chosen), select which to highlight, and read both results.
Step-by-Step Example Calculation
Choose 3 from 10
Input Values:
n:10
r:3
mode:combination
Worked Steps: C(10,3) = 120 combinations; P(10,3) = 720 permutations.
Understanding Your Result
P(n,r) > C(n,r) since each combination corresponds to r! permutations.
Factors That Affect the Result
- When r = 1, P = C = n. When r = n, P = n! and C = 1.
When Should You Use This Calculator?
- Lottery odds, tournament schedules, password counting, genetics.
Assumptions & Limitations
- n must be ≤ 170 (JavaScript number precision limit for factorials).
Frequently Asked Questions
Calculation Accuracy & Reference Note
Uses exact double-precision floating-point factorial for n ≤ 170.