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{{ printedBook.courseTrack.name }} {{ printedBook.name }} A **combination** is a selection of elements from a set where the order in which they are selected is not important. Therefore, the only important thing is which elements are selected. For example, choosing two different ingredients for a salad from five unique options in the salad bar.

When counting the number of possible combinations, either:

- every possibility must be listed and counted or
- the
*Combination Formula*can be used.

This formula calculates the number of combinations $C$ that can be done by using $n$ elements of a set to form groups of $r$ elements. Note that the exclamation points in the formula indicate that the factorial of the value should be calculated.

$_{n}C_{r}=(n−r)!r!n! $

In the salad bar example, there were $n=5$ options provided to make groups of $r=2.$

$_{5}C_{2}_{5}C_{2}_{5}C_{2}_{5}C_{2}_{5}C_{2} =(5−2)!2!5! =3!2!5! =3 ⋅2 ⋅1 ⋅2⋅15⋅4⋅3 ⋅2 ⋅1 =220 =10 $

An alternate notation for $_{n}C_{r}$ is $C(r,n).$