### Binomial coefficient

The binomial coefficients arise when developing the successive terms in the binomial theorem

The number *n* is the power of the binomial theorem, the number *r* is the current number of the term in the outcome.

##### Explanation

We write the binomial expansion and see

It contains a clear regularity. Each term has the general form

Coefficient ×

a^{n−r}b^{r}

in which

n= power of the binomium

r= number of the term

The expansion of the coefficients follows Pascal's triangle. A number is formed by the sum of the number there just above left and right

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1

In each row the numbers increase, and then decrease in the same way. They can be calculated with the formula for combinations

in which

n= power of the binomium

r= number of the term