Binomial Coefficient Calculator





Formula

The formula to calculate the binomial coefficient is:

\[ C(n, k) = \frac{n!}{k!(n-k)!} \]

Where:

What is a Binomial Coefficient?

A binomial coefficient is the total number of combinations that can be made from any set of integers. It represents the number of ways to choose \( k \) items from \( n \) items without regard to the order of selection.

Example Calculation

Let's assume the following values:

Step 1: Calculate the factorials:

\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]

\[ 2! = 2 \times 1 = 2 \]

\[ (5-2)! = 3! = 3 \times 2 \times 1 = 6 \]

Step 2: Calculate the Binomial Coefficient \( C(5, 2) \):

\[ C(5, 2) = \frac{5!}{2!(5-2)!} = \frac{120}{2 \times 6} = \frac{120}{12} = 10 \]

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