Permutation & Combination Calculator
Calculate permutations and combinations.
Calculation Parameters
Total number of items
Number to arrange/select (r ≤ n)
Result
Permutation
60
P(5, 3)
Type
Order Matters
Formula:
P(5, 3) = 5! / (5 - 3)! = 60
About This Calculator
The Permutation and Combination Calculator helps you calculate the number of ways to arrange (permutations) or select (combinations) items from a set. Permutations consider order, while combinations do not.
Use permutations when order matters (e.g., arranging people in a line, password arrangements). Use combinations when order doesn't matter (e.g., selecting team members, choosing lottery numbers). The calculator uses factorial calculations to determine the number of possibilities.
Formula & Calculation Method
Permutation and Combination Formulas:
Permutation (Order Matters):
P(n,r) = n! / (n-r)!
Number of ways to arrange r items from n items
Combination (Order Doesn't Matter):
C(n,r) = n! / (r! × (n-r)!)
Number of ways to select r items from n items
Factorial:
n! = n × (n-1) × (n-2) × ... × 2 × 1
0! = 1
Permutations give more results than combinations because order matters. For example, P(5,3) = 60 (arrangements of 3 items from 5), while C(5,3) = 10 (selections of 3 items from 5, order doesn't matter).
How to Use This Calculator
- Select Type: Choose Permutation (order matters) or Combination (order doesn't matter).
- Enter n: Input the total number of items in the set.
- Enter r: Input the number of items to arrange or select (r ≤ n).
- View Results: See the calculated number of permutations or combinations.
Frequently Asked Questions
What is the difference between permutation and combination?
Permutation considers order (ABC is different from BAC), while combination does not (ABC is the same as BAC). Permutations give more results. For example, arranging 3 people from 5 gives 60 permutations but only 10 combinations.
When should I use permutations?
Use permutations when order matters: arranging people in a line, creating passwords, scheduling events in order, ranking items. Any situation where the sequence/arrangement is important.
When should I use combinations?
Use combinations when order doesn't matter: selecting team members, choosing lottery numbers, forming committees, picking items from a group. The selection is what matters, not the order.
Why is there a limit on n?
Factorials grow very rapidly. 170! is the largest factorial that can be accurately represented in standard JavaScript. For larger values, approximate methods or specialized libraries are needed.
Calculator by
NumCalculators Editorial Team
Multi-disciplinary Expert Team