Permutations and combinations

Different orders of placing n elements into n places, one per place, are called permutations. Their number is Pₙ = n · (n - 1) · ... · 2 · 1 = n! (n factorial). For example, 4 books can be placed on a shelf in P₄ = 4! = 24 different orders. In combinations of n elements taken k at a time the order does not matter, only the content does; their number is denoted Cₙᵏ and is found by Cₙᵏ = n!/(k! (n - k)!) = n(n - 1)...(n - k + 1)/k!. For example C₅² = 5 · 4/(1 · 2) = 10. The equality Cₙᵏ = Cₙⁿ⁻ᵏ holds: choosing k elements is the same as leaving out the other n - k. If order matters we use permutations; if not, combinations.