Online Combinations Calculator

What Is This Tool?

The Combination Calculator works out nCr, the number of ways to choose a sample of r items from a set of n items when the order of selection does not matter. You enter the total number of objects and the sample size, and it returns the exact count, using high-precision big-number arithmetic so even large sets produce accurate results. It accepts whole numbers with n greater than or equal to r, and the result can be downloaded as a PDF.

How to Use This Tool?

• Enter the total number of objects, n.
• Enter the sample size, r, making sure it is no larger than n.
• Click Calculate to see the number of combinations.
• Click Download Result as PDF to save a copy.

Key Features

• Calculates combinations (nCr) for a chosen number of objects and sample size.
• Uses high-precision big-number arithmetic for accurate results on large inputs.
• Validates that both values are whole numbers with n at least as large as r.
• Shows the result instantly as you calculate.
• Download the result as a PDF.

Examples

• Choosing 2 from 4 items gives 6 combinations.
• Choosing 3 from 5 items gives 10 combinations.
• Choosing 5 cards from a 52-card deck gives 2,598,960 possible hands.
• Choosing 0 from any set gives exactly 1 combination, the empty selection.

Common Use Cases

• Working out probabilities where the order of items does not matter.
• Estimating lottery or card-hand counts.
• Counting the ways to form a committee or group from a larger pool.
• Solving probability and statistics homework problems.
• Checking combinatorics results quickly without manual factorials.

Tips & Best Practices

• Make sure the sample size r is no larger than the total n.
• Enter whole numbers only, since combinations are defined for integers.
• Use this tool when order does not matter, and a permutation tool when it does.
• Remember that choosing r or choosing n minus r gives the same count.
• For very large sets, expect an extremely long number as the answer.

Limitations

• It only accepts non-negative whole numbers for n and r.
• It counts combinations only, where order does not matter, not ordered permutations.
• Extremely large results are shown in a shortened exponential form rather than full digits.
• It returns the count of combinations, not a list of the actual selections.

Frequently Asked Questions

What is the difference between a combination and a permutation?

A combination counts selections where order does not matter, while a permutation counts arrangements where the order does matter.

How is nCr calculated?

It equals n factorial divided by the product of r factorial and n minus r factorial.

Can n or r be zero?

Yes. Choosing 0 items gives 1 combination, and the tool accepts 0 as long as n is at least as large as r.

Can I save my result?

Yes. Click Download Result as PDF to save the calculation as a file.

Key Terminology

Combination

A selection of items from a set where the order of selection does not matter.

Permutation

An arrangement of items where the order does matter.

Factorial

The product of all positive integers up to a number, written with an exclamation mark.

nCr

Standard notation for the number of combinations of r items chosen from n.

Sample size

The number of items being chosen from the larger set, r in nCr.

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