Permutations and Combinations Basics A permutation is an ordered arrangement of n elements. For example, the permutation of the digits 1, 2, and 3 is 123, wh...
A permutation is an ordered arrangement of n elements. For example, the permutation of the digits 1, 2, and 3 is 123, while the permutation of the letters A, B, and C is ABC.
A combination is a subset of n elements that are selected without regard to order. For example, the combinations of the digits 1, 2, and 3 are {1, 2, 3}, while the combinations of the letters A, B, and C are {AB, AC, BC}.
The formula for the number of permutations of n elements is n! This means that the number of permutations of n elements is the product of all the permutations of n-1 elements. For example, the number of permutations of 5 elements is 5! = 5 x 4 x 3 x 2 x 1 = 120.
The formula for the number of combinations of n elements is n!/(n - r)! This means that the number of combinations of n elements with r elements is the product of all the permutations of n-r elements. For example, the number of combinations of 5 elements with 2 elements is 5!/(5 - 2)! = 10.
Permutations and combinations are used in a variety of mathematical and real-world problems. For example, in probability theory, permutations and combinations are used to calculate the probability of different outcomes in a given experiment. In combinatorics, permutations and combinations are used to determine the number of different ways to select a subset of a set