Permutation refers to possible arrangements of objects when order matters. Permutation formula: P(n,r) = n!/(n-r)!. Permutation is used when order of selection matters
Permutation counts different arrangements from given set of things. Combination counts different groups from given set of things. Order matters in permutations, order doesn't in combinations
Derangement is a permutation where no element appears in its original position. Number of derangements is called subfactorial of n or nth derangement number. Common notations include !n, Dn, dn, or n¡
Permutation arranges objects in sequence, while combination selects items without order. Permutations occur in almost every area of mathematics. Combinations can be counted in smaller cases
Combinations count k items from n items with or without repetition. Permutations are n-element ordered groups without repetition. Variations are ordered groups with non-repeating elements
Factorial of n is product of all positive integers up to n. Zero factorial (0!) equals 1. Factorial can be represented as recursive function. Factorial of negative numbers is undefined