Permutation & Combination

A permutation P(n,r) counts the number of ways to arrange r items from n, calculated as n!/(n-r)!. A combination C(n,r) counts the number of ways to choose r items from n regardless of order, calculated as n!/(r!(n-r)!). Repeated permutations allow the same item to be chosen multiple times (n^r), while repeated combinations H(n,r) = C(n+r-1,r) allow choosing with repetition without regard to order.

Real-world applications include selecting leadership (permutations for rank-ordered positions), lottery drawings and grouping tasks (combinations where order is irrelevant), password generation (repeated permutations allowing repeated characters), and sampling with replacement (repeated combinations). This tool computes all four values instantly by entering n and r, displaying the formulas. It is ideal for probability and statistics education, combinatorics in programming, data analysis, and various mathematical problem-solving scenarios.