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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