Math basics › Probability and statistics

Permutations and combinations

Does order matter?

That one question decides it. Arranging, ranking, codes: order matters. Choosing a team or a hand of cards: it does not.

nPr = n!/(n − r)!, the ways to arrange r things out of n.

nCr = n!/(r!(n − r)!), the ways to choose r things out of n. It is the permutations divided by the r! orders that now count as the same.

3 shirts and 4 pairs of pants make 3 × 4 = 12 outfits.