Combination Calculator (nCr)

Calculate the number of ways to choose r items from n items without repetition and without order. Essential for probability, statistics, and combinatorics problems.

Total Items (n)

Items to Choose (r)

Result

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Combination Visualizer

Items to choose (r) 3

Enter n to visualize combinations

Understanding Combinations

Combinations calculate the number of ways to select items from a collection where order does not matter. Used in probability calculations, lottery odds, and experimental design.

Calculation Formula

nCr = n! / (r! × (n - r)!) where n ≥ r ≥ 0

Example Calculation

For n=5, r=3: 5C3 = 5! / (3! × 2!) = 120 / (6 × 2) = 10

Reference Table

n	r=2	r=3	r=4
4	6	4	1
5	10	10	5
6	15	20	15

Frequently Asked Questions

What if r is greater than n?

The result is 0 since you cannot choose more items than available.

How are decimal inputs handled?

Decimal values are truncated to integers. Only non-negative integers are valid.

What is the maximum n value supported?

Up to n=170 due to JavaScript number precision limitations.

Disclaimer: For informational and educational purposes only. Results may vary due to rounding and computational limitations.

References

Binomial coefficient properties · Combinatorial mathematics · Probability theory fundamentals

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Combination nCr Calculator - Choose Without Order

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