Changes

For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.

For example, take a race which has 10 competitors. There are 10 choose 3 different combinations of medal winners (that is, racers who get either 1st, 2nd, or 3rd place), which is a total of 10! / (10 - 3)! • 3! = 10! / 7! • 3! = 120 different combinations.

The numbers <math>\begin{pmatrix} n \\ r \end{pmatrix}</math> are also called binomial coefficients because of the expansion:

The numbers <math>\begin{pmatrix} n \\ r \end{pmatrix}</math> are also called binomial coefficients because of the [[binomial expansion]]:

:<math>(x + y)^n = \sum_{r = 0}^n \begin{pmatrix} n \\ r \end{pmatrix} x^r y^{n-r}</math>

:<math>(x + y)^n = \sum_{r = 0}^n \begin{pmatrix} n \\ r \end{pmatrix} x^r y^{n-r}</math>