A **combination** is the number of ways a given number of objects can be selected from a group when the order does not matter (unlike a permutation, in which order does matter). If *k* objects are selected from a group of *n* members, the formula for the combination (which can be read as "n choose k") is

Combinations are important in probability as well as to the binomial theorem. All the possible combinations of an integer *n* make up the *n*th row of Pascal's triangle.

## Formulas[]

Since picking which to use is the same as picking which not to use.

Only 1 option, none of them.

Since you pick 1 of them.

## Example[]

How many different groups of three can be chosen from five people?

Since order is not important, we can use the formula for a combination.

## Practice[]

Henry wants to choose 3 out of his 7 friends, how many ways can he do this?

Joe wants to choose 4 out of his 6 friends to go fishing with him. However, Jimmy and Andrew do not get along so they cannot be chosen together. How many ways can he do this?