Permutation & Combination Calculator

Calculate nPr (Permutations) and nCr (Combinations) | Step-by-step solutions

Result (nPr)
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📝 Step-by-step solution
Enter values and click calculate.
📖 What does this mean?
Permutations count the number of ways to arrange r items out of n distinct items where order matters.

📖 How to Use This Calculator

1
Choose calculation type - Select Permutation (nPr) where order matters, or Combination (nCr) where order doesn't matter.
2
Enter total items (n) - The total number of distinct items available.
3
Enter chosen items (r) - How many items you want to arrange or select.
4
Click "Calculate" - Get the result with step-by-step explanation.

🔢 Understanding Permutations vs Combinations

Permutations (nPr) count the number of ways to arrange r items from n distinct items where order matters. Example: Arranging 3 books on a shelf - ABC is different from CBA.

Combinations (nCr) count the number of ways to select r items from n distinct items where order does NOT matter.

🧮 Formulas

Permutation (nPr): nPr = n! / (n - r)!
Combination (nCr): nCr = n! / (r! × (n - r)!)
Key relationship: nPr = nCr × r!

📊 Real-World Examples

❓ Frequently Asked Questions

What is the main difference between permutation and combination?
In permutations, order matters. In combinations, order does not matter.
When should I use nPr vs nCr?
Use nPr when order matters (passwords, race rankings). Use nCr when only selection matters (lottery numbers).
What does factorial (!) mean?
A factorial (n!) is the product of all positive integers from 1 to n. Example: 5! = 120.
Can r be greater than n?
No, you cannot choose more items than are available. If r > n, the result is 0.