User:HelpJazz/workspace

Combinations

It is often useful to find out how many groups of r objects can be created out of a group of n objects. This can be calculated from a function called "choose" (read aloud as "n choose r"):

$={\binom {n}{r}}{\frac {n!}{(n-r)!r!}}$

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.