Calculating Binomial Coefficient: Enhanced Explanation and Examples

Find the binomial coefficient.C= (3)…….(2)

To find the binomial coefficient, we need to use the formula for the factorial

To find the binomial coefficient, we need to use the formula for the factorial. The factorial of a number is denoted by the exclamation mark (!) and is the product of all positive integers less than or equal to that number.

For example, the factorial of 4 is written as 4! and calculated as:

4! = 4 × 3 × 2 × 1 = 24

In this case, we are given the expression C = (3)(2) and we need to find the binomial coefficient.

The binomial coefficient is represented as C(n, k), where n is the total number of items and k is the number of items being selected. It can be calculated using the formula:

C(n, k) = n! / (k! * (n – k)!)

So, extrapolating this to our given expression C = (3)(2), we can say that n = 3 and k = 2. Substituting these values into the binomial coefficient formula, we get:

C(3, 2) = 3! / (2! * (3 – 2)!)

Now, let’s calculate the factorial values.

3! = 3 × 2 × 1 = 6
2! = 2 × 1 = 2
3 – 2! = 1! = 1

Substituting these values into the formula, we have:

C(3, 2) = 6 / (2 * 1)
= 6 / 2
= 3

Therefore, the binomial coefficient C = (3)(2) is equal to 3.

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