Permutation Combination Calculator

Permutation & Combination Calculator – Instantly calculate the number of ways to arrange (nPr) or choose (nCr) objects. Great for probability, statistics, and math problems.

Permutation Combination Calculator Permutation Combination Calculator

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Description

🔢 Permutation & Combination Calculator – Count Arrangements & Selections

The Permutation & Combination Calculator helps you quickly solve problems related to arranging or selecting objects. It’s widely used in probability, statistics, and combinatorics for counting possible outcomes.

📘 What It Calculates:

  • ✅ Permutations (nPr): Number of ways to arrange objects in order

  • ✅ Combinations (nCr): Number of ways to choose objects without considering order

  • ✅ Works for small and large numbers

💡 Features:

  • Easy input (n = total items, r = chosen items)

  • Calculates both nPr and nCr instantly

  • Step-by-step explanation of formulas

  • Useful in probability, arrangements, and statistics

👤 Who Should Use This:

  • 📌 Students learning combinatorics & probability

  • 📌 Teachers & tutors explaining arrangements

  • 📌 Professionals solving probability/statistics problems

  • 📌 Anyone needing quick arrangements/selections calculations

✅ Pro Tip:

  • Permutation formula (order matters):

nPr=n!(n−r)!nPr = \frac{n!}{(n-r)!}nPr=(n−r)!n!​

  • Combination formula (order doesn’t matter):

nCr=n!r!(n−r)!nCr = \frac{n!}{r!(n-r)!}nCr=r!(n−r)!n!​

🔗 Related Tools:

5 𝑃 3 = 5 ! ( 5 − 3 ) ! = 120 2 = 60 5P3= (5−3)! 5! ​ = 2 120 ​ =60

In permutations, the order of objects matters (arrangements). In combinations, the order does not matter (selections).

Factorial represents the product of all positive integers up to a number. Since permutations and combinations involve arranging or choosing multiple items, factorial helps calculate all possible arrangements systematically.

No. Since permutations consider order and combinations do not, the number of permutations is always greater than or equal to the number of combinations.