Answer: Sure, I can help you with that! Here's a step-by-step guide on how to calculate the binomial coefficient C(n, k) using the formula:
C(n, k) = n! / (k! * (n - k)!)
where "!" denotes the factorial function.
Step 1: Input the values of n and k.
Let's say you want to calculate C(5, 2), which is the binomial coefficient of choosing 2 items from a set of 5 items. In this case, n = 5 and k = 2.
Step 2: Calculate k! and (n - k)!
In our example, k = 2, so k! = 2! = 2 * 1 = 2, and (n - k) = (5 - 2) = 3, so (n - k)! = 3! = 3 * 2 * 1 = 6.
Step 3: Calculate n!
n! = 5 * 4 * 3 * 2 * 1 = 120
Step 4: Calculate C(n, k)
C(n, k) = n! / (k! * (n - k)!) = 120 / (2 * 6) = 120 / 12 = 10
Therefore, C(5, 2) = 10, which means there are 10 ways to choose 2 items from a set of 5 items.
Explanation: