Permutation & Combination Calculator
If you are searching for a fast, accurate, and easy-to-use Permutation & Combination Calculator, then this page gives you everything you need—instant nPr calculation, nCr calculation, step-by-step working, factorial breakdown, and a complete math explanation with examples. Whether you are a student, teacher, competitive exam aspirant, or someone working on statistics / probability projects, this advanced permutation calculator helps you compute results instantly.
Below, we also explain what is permutation, what is combination, difference between permutation and combination, formulas, shortcut tricks, and more.
This makes the entire page highly indexable for Google Search, fully optimized with rich keywords, and helpful for the user.
Permutation & Combination Calculator
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What is a Permutation & Combination Calculator?
A Permutation & Combination Calculator is an online tool that helps you calculate:
- Permutation (nPr) – when order matters
- Combination (nCr) – when order does NOT matter
The calculator automatically computes:
- nPr = n! / (n-r)!
- nCr = n! / [r! × (n − r)!]
- Factorial breakdown (n!, r!, (n−r)!)
- Step-by-step solution for students
- Instant final result with proper formatting
It works for math students, statistics, probability, combinatorics, JEE, NEET, banking exams, and more.
Why Use Our Advanced Permutation & Combination Calculator?
- Professional math formatting
- Live formula substitution
- Easy input boxes for n and r
- Radio switch for nPr / nCr
- Highlighted final answer in red box
- Step-by-step breakdown for better understanding
This makes it ideal for:
➡ Students solving math homework
➡ Teachers explaining problems
➡ Aspirants preparing for JEE, NEET, SSC, IBPS, CAT, etc.
➡ Anyone wanting quick permutation and combination solutions
Understanding Permutations (nPr)
A permutation refers to the arrangement of objects where order matters.
✔ Permutation Formula
nPr = n! / (n − r)!
✔ Example (Easy to index & understand)
You have 5 books, and you want to arrange 3 of them on a shelf:
5P3 = 5! / 2! = 120 / 2 = 60 arrangements
This shows how order changes total outcomes.
Understanding Combinations (nCr)
A combination means selecting items without caring about order.
✔ Combination Formula
nCr = n! / [r! × (n − r)!]
✔ Example
You have 5 players, and you want to choose 3 for a team:
5C3 = 5! / (3! × 2!) = 120 / (6 × 2) = 10 selections
Order doesn’t matter here.
Difference Between Permutation and Combination
| Feature | Permutation (nPr) | Combination (nCr) |
|---|---|---|
| Order matters? | ✔ Yes | ❌ No |
| Formula | n! / (n − r)! | n! / (r! × (n − r)!) |
| Use case | Arrangements | Selections |
| Example | Placing books in order | Choosing a team |
How the Calculator Works ?
When users enter values for n and r, the calculator:
1. Validates the input
- Ensures
n ≥ r - Ensures values are non-negative
2. Detects selected mode
- Permutation (nPr)
- Combination (nCr)
3. Shows step-by-step solution
Including:
- Formula identification
- Substitution
- Factorial expansion
Final evaluation
4. Shows final answer with proper formatting
This improves user experience and SEO value.
Where Are Permutations & Combinations Used?
✔ Real-life applications
- Assigning ranks
- Arranging seats
- Lottery selections
- Password combinations
- Tournament teams
- Probability problems
- Statistics
- Data science
- Computer algorithms
- Machine learning models
Formula Breakdown
Permutation Formula (nPr) Keywords
- nPr calculator
- Permutation formula
- Factorial-based permutation
- Order-based arrangement
Combination Formula (nCr) Keywords
- nCr calculator
- Combination formula
- Selection without order
- Combinatorics calculation
Example Problems
🔹 Example 1 (Permutation)
How many ways can 8 runners finish in 3 positions?
8P3 = 8! / 5! = 336
🔹 Example 2 (Combination)
How many ways to choose 4 students out of 12?
12C4 = 495
🔹 Example 3 (Large nPr)
20P2 = 20! / 18! = 380
🔹 Example 4 (Large nCr)
30C5 = 142506
Advantages of Using an Online Permutation & Combination Calculator
- ✔ Saves time
- Manual factorial calculations take long.
- ✔ Avoids mistakes
- Large numbers cause human error.
- ✔ Mobile-friendly
- Works perfectly on small screens.
- ✔ Shows complete steps
- Great for learning and exams.
- ✔ Free to use
- No login, no signup.
Frequently Asked Questions (FAQ) – Typing Speed Calculator
- Qns 1: What is permutation in simple words?
- Permutation means arranging items where order matters.
- Qns 2: What is combination in simple words?
- Combination means selecting items without considering order.
- Qns 3: What is nPr?
- nPr denotes permutation: n! / (n − r)!.
- Qns 4: What is nCr?
- nCr denotes combination: n! / (r! × (n − r)!).
- Qns 5: Where are permutations used?
- Used in arrangements, ranking, probability, and ordering.
- Qns 6: Where are combinations used?
- Used in choosing teams, lotteries, and probability selections.
- Qns 7: Can this calculator handle large numbers?
- Yes, it calculates large factorial values instantly.
- Qns 8: Is this tool free?
- Yes, 100% free and online.ns
Conclusion
This Permutation & Combination Calculator is one of the most accurate and easy-to-use online tools for solving nPr, nCr, factorials, and combinatorics problems. Whether you’re solving probability, statistics, math assignments, or preparing for competitive exams, this tool provides instant results, step-by-step working, and clear explanations. Use this calculator anytime you need to compute:
- Permutation (nPr)
- Combination (nCr)
- Factorial values
- Arrangement and selection problems
Search Keywords
Permutation calculator, nPr calculator, Combination calculator, nCr calculator, factorial calculator online, permutation and combination formulas, math calculator, probability calculator, arrangement calculator, selection calculator, combinatorics calculator
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