Permutation & Combination Calculator
Enter values for n and r to calculate permutations and combinations.
Results:
Permutation and Combination Calculator: Calculate Arrangements and Selections Easily
Intro
A Permutation and Combination Calculator is a handy online tool that helps you solve problems involving arrangements and selections of objects. Instead of memorizing formulas or struggling with large factorials, this tool gives you quick and accurate results in seconds.
- Permutation: The arrangement of items where order matters.
- Combination: The selection of items where order does not matter.
This calculator is especially useful for students, teachers, statisticians, researchers, and anyone dealing with probability, statistics, or combinatorics. Whether you’re solving exam questions or analyzing real-world scenarios like lottery draws or seating arrangements, the Permutation and Combination Calculator online makes the process simple.
Formula / Working
Permutation Formula
P(n,r)=n!(n−r)!P(n, r) = \frac{n!}{(n-r)!}P(n,r)=(n−r)!n!
Where:
- nnn = total number of items
- rrr = number of items chosen
- !!! = factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1)
Combination Formula
C(n,r)=n!r!(n−r)!C(n, r) = \frac{n!}{r!(n-r)!}C(n,r)=r!(n−r)!n!
Where:
- nnn = total number of items
- rrr = number of items selected
- Order does not matter
The calculator uses these formulas automatically, so you just enter nnn and rrr to get instant results.
Step-by-Step Usage
Using the Permutation and Combination Calculator online is very simple:
- Enter the total number of items (n).
- Enter how many items you want to select (r).
- Choose whether you want to calculate Permutation (P) or Combination (C).
- Click “Calculate” to get the result instantly.
Examples
Example 1: Permutation (Order Matters)
How many ways can 3 people be arranged in 5 seats? P(5,3)=5!(5−3)!=5×4×3×2×12!=60P(5, 3) = \frac{5!}{(5-3)!} = \frac{5 \times 4 \times 3 \times 2 \times 1}{2!} = 60P(5,3)=(5−3)!5!=2!5×4×3×2×1=60
Result: There are 60 different ways to arrange 3 people in 5 seats.
Example 2: Combination (Order Does Not Matter)
How many ways can 2 fruits be chosen from 4 (Apple, Banana, Mango, Orange)? C(4,2)=4!2!(4−2)!=242×2=6C(4, 2) = \frac{4!}{2!(4-2)!} = \frac{24}{2 \times 2} = 6C(4,2)=2!(4−2)!4!=2×224=6
Result: There are 6 different ways to select 2 fruits out of 4.
Example 3: Larger Numbers
If you want to select 6 lottery numbers out of 49, the number of possible combinations is: C(49,6)=49!6!(49−6)!=13,983,816C(49, 6) = \frac{49!}{6!(49-6)!} = 13,983,816C(49,6)=6!(49−6)!49!=13,983,816
Result: There are 13,983,816 possible outcomes in a 6/49 lottery game.
FAQs
Q1. What is the difference between permutation and combination?
Permutation considers order important, while combination does not.
Q2. Can this calculator handle large numbers?
Yes, the Permutation and Combination Calculator online can calculate very large factorials instantly.
Q3. Where are permutations and combinations used in real life?
They’re used in probability, statistics, game theory, cryptography, lottery systems, seating arrangements, and more.
Q4. Do I need to remember formulas?
No, the calculator applies formulas automatically. You just need to input the values.
Q5. Can I use this tool for exams or homework?
Yes, it’s an excellent learning aid for students studying mathematics, statistics, or probability.