Combinations & Permutations Calculator

Calculate nCr, nPr, and versions with repetition – instantly

Permutations (Order Matters)

P(10,3) = 720

nPr = n × (n-1) × ... × (n-r+1)

Combinations (Order Doesn't Matter)

C(10,3) = 120

nCr = n! / (r! × (n-r)!)

Current Formula

P(10,3) = 10 × 9 × 8

C(10,3) = 10! / (3! × 7!)

Combinations & Permutations Calculator – Master Counting and Probability Problems

Our advanced Combinations and Permutations Calculator is the ultimate tool for students, teachers, statisticians, data scientists, and anyone working with probability, combinatorics, or counting problems. Instantly calculate nCr (combinations), nPr (permutations), and versions with repetition — with clear formulas and step-by-step explanations.

Whether you're solving lottery odds, arranging passwords, selecting teams, analyzing survey data, or studying discrete mathematics, this calculator delivers accurate results in milliseconds. Understand the difference between order mattering (permutations) and not mattering (combinations) with real-world examples.

Why Use Our Combinations & Permutations Calculator?

Instant Results

No manual factorial calculations — get nCr and nPr in milliseconds.

With Repetition Support

Calculate arrangements where items can be repeated (e.g., PIN codes).

Educational Tool

Perfect for learning discrete math, probability, and statistics concepts.

Real-World Applications

Lottery odds, password strength, team selection, survey sampling, and more.

How to Use the Calculator

1

Enter n and r

n = total number of items, r = number to choose or arrange.

2

Check "With Repetition" if needed

Use for passwords, PINs, or when items can repeat.

3

Get Instant Results

See both permutations and combinations with formulas.

Frequently Asked Questions

When to use combinations vs permutations?

Use permutations when order matters (e.g., arranging people in a line, passwords). Use combinations when order doesn't matter (e.g., selecting a committee, lottery numbers).

What does "with repetition" mean?

It means the same item can be chosen more than once. Example: forming a 4-digit PIN where digits can repeat (1111 is allowed).

How is C(n,r) related to P(n,r)?

C(n,r) = P(n,r) ÷ r! → Because permutations count all orders, but combinations treat all orders of the same items as one.

Popular Search Terms

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