Permutations and combinations

Permutations and combinations, mathematical term for ways of counting out, arranging, and choosing objects in a group. A permutation is simply a way in which the elements of a set can be ordered. For instance, a set of 3 objects—say the numbers 1, 2, and 3—can be arranged in 6 different ways: 123, 132, 231, 213, 312, and 321. Each of these is a permutation. A combination is a choice of a certain number of elements from a larger set, without regard to the order of the elements. For instance, given the same set—1, 2, and 3—we may be asked to pick 2 out of the 3 numbers. Here there are 3 possibilities: 1 and 2, 1 and 3, 2 and 3. In other words, there are 3 different ways of picking 2 elements out of a set of 3 elements. Each different way is a combination. The techniques of permutations and combinations are of central importance in problems of probability and statistics.