^{n}C_{0}, ^{n}C_{1}, ^{n}C_{2}, ^{n}C_{3},….. ^{n}C_{r}… ^{n}C_{n} are called Binomial Coefficients.

Recall the formula for factorial of a number n defined as

n! = n (n – 1) (n - 2 ) (n - 3) (n - 4)……3.2.1

For Eg,

5;! = 5.4.3.2.1 = 120

4;! = 4.3.2.1 = 24

3;! = 3.2.1 = 6

2;! = 2.1= 2

1;! = 1 and note that

0;! = 1

The values of the Binomial Coefficients are determined by the following formula: