Binomial coefficients

 Binomial coefficients: -

 

-Binomial coefficients represent the number of ways to choose k items from a set of n distinct items.

-Binomial coefficients have various applications in combinatorics, probability theory, algebra, and many other areas of mathematics and computer science.

-The formula for binomial coefficients is:

                       

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

Where:

 

--> C(n, k) is the binomial coefficient.

--> n! represents the factorial of n, which is the product of all positive integers from 1 to n.

--> k! represents the factorial of k.

--> (n - k)! represents the factorial of (n - k).

Ex.

-Suppose you have a group of 6 different books, and you want to know how many ways you can choose 3 books from this group to read over the weekend.

            C(6, 3) = 6! / (3!(6 - 3)!)

            C(6, 3) = (6 * 5 * 4) / (3 * 2 * 1)

            C(6, 3) = 20

So, there are 20 different ways you can choose 3 books from the set of 6 for your weekend.