Choosing three toppings for a pizza from a list of eight is a combination. The order you name them does not matter; pepperoni, mushroom, and onion is the same pizza as onion, pepperoni, and mushroom. Combinations count selections, not arrangements.

The number of ways to choose r items from n is written C(n, r) or nCr, and equals n! / (r!(n − r)!). For the pizza example, C(8, 3) = 56. The formula divides out the r! orderings that would matter in a permutation.

Combinations appear in card games, lottery odds, committee selection, and probability problems. They also underlie the binomial theorem and Pascal's triangle. The distinction between combinations and permutations is one of the first lessons in combinatorics, and it trips up many students until the idea clicks.

• Selection where order does not matter
• Formula: n! / (r!(n − r)!)
• Distinct from permutations
• Used in probability, games, and the binomial theorem