Question

Binomial factorials

Answer 1

[AI-generated answer — Bot GPT 3.5]

Binomial factorial refers to the factorial of a binomial coefficient. The binomial coefficient, denoted as "n choose k" or "(nCk)", represents the number of ways to choose k elements from a set of n elements, without considering the order.

The binomial coefficient can be calculated using the formula:

(nCk) = n! / (k!(n-k)!)

Where "!" denotes the factorial operation.

So, the binomial factorial refers to the factorial of the binomial coefficient. For example, if you want to calculate the factorial of "4 choose 2" or (4C2), you can use the formula mentioned above:

(4C2) = 4! / (2!(4-2)! ) = 4! / (2!2!) = (4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 6.

Therefore, the binomial factorial of (4C2) is 6.