Calculation of Binomial Coefficient C(n, r) Using Combination Formula: Step-by-Step Process

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

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

To find the binomial coefficient, we need to use the formula for combination. The combination formula is given by:

C(n, r) = n! / (r!(n-r)!)

In this case, we are given C = (3)…….(2). From this, we can gather that we are evaluating C(3,2).

Using the combination formula, we can substitute n = 3 and r = 2:

C(3, 2) = 3! / (2!(3-2)!)

Simplifying further:

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

Note that 3! means factorial of 3, which is the product of all positive integers from 1 to 3:

3! = 3 * 2 * 1 = 6

Similarly, 2! means factorial of 2:

2! = 2 * 1 = 2

1! is defined as 1.

Substituting these values back into the formula:

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

Simplifying:

C(3, 2) = 6 / 2

C(3, 2) = 3

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

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