Binomial Coefficient Calculator

What is the Binomial Coefficient?

The Binomial Coefficient Calculator is a tool that helps you calculate the binomial coefficient, denoted as \( C(n, k) \) or \( \binom{n}{k} \). This coefficient is used to determine the number of ways to choose \( k \) elements from a set of \( n \) elements without considering the order.

The binomial coefficient is calculated using the following formula:

Where:

• \( n! \): The factorial of \( n \) (product of all positive integers up to \( n \)).
• \( k! \): The factorial of \( k \).
• \( (n-k)! \): The factorial of \( n-k \).

Example

Let’s calculate \( C(5, 2) \):

The binomial coefficient \( C(5, 2) \) is 10.

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