Use this binomial coefficient calculator to quickly determine the number of ways you can choose a subset of items from a larger set.

## Binomial Coefficient Calculator

### How to Use the Calculator

Enter a non-negative integer for **n** which represents the total number of items, and a non-negative integer for **k** which represents the number of items to choose from the set of **n** items. Then click on the “Calculate” button to see the binomial coefficient result.

### How the Calculator Works

The binomial coefficient, also known as a combination or combinatorial number, calculates the number of ways to choose a set of **k** elements from a set of **n** elements without regard to the order of selection. This is commonly represented as “n choose k” and mathematically defined as C(n, k) = n! / (k!(n-k)!), where “!” denotes the factorial operation.

### Limitations of the Calculator

This calculator uses standard JavaScript which handles number calculations using floating point arithmetic, which can introduce rounding errors for very large numbers. Also, due to limitations on the maximum safe integer that JavaScript can represent accurately (2^{53} – 1), inputs for very large values of **n** or **k** may result in inaccurate computations or overflow errors. It’s best used for smaller, more practical combinations where high precision isn’t critical.

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