The formula to calculate the binomial coefficient is:
\[ C(n, k) = \frac{n!}{k!(n-k)!} \]
Where:
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.
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.
