Combinatorics is a branch of mathematics that deals with the study of discrete structures and the enumeration of arrangements and selections. Combinatorics is concerned with counting and arranging objects or events, which has applications in computer science, cryptography, probability, statistics, and various other areas. In network theory, combinatorics helps in analyzing connectivity, paths, and cycles in graphs.
Combinatrix is a simple Python library that provides functions to calculate the number of permutations and combinations of a set of items. With Combinatrix, you can now effortlessly calculate the number of ways to arrange or select items from a set of choices in your Python projects.
Combinatrix contains a single function called calc_permutations_combinations, which takes the number of possible choices, the number of choices to make, and an optional flag to allow repetitions, and returns the number of combinations and permutations.
number_of_possible_choices(int): Total number of possible choices.number_of_choices_to_make(int): Number of choices to make.allow_repetitions(bool, optional): IfTrue, repetition of a choice is allowed. Defaults toTrue.
- (tuple): A tuple containing two integers - (combinations, permutations).
A permutation is an arrangement of items in a specific order i.e., represents the number of ways we can select r items from a set of n items when the ordering of the selection does matter. The formula to calculate permutations is:
nPr = n! / (n - r)!
where n is the total number of items, r is the number of items to select, and ! represents the factorial function.
A good example of permutations is a combination lock. A combination lock has a set of n numbers (0-9) and a combination of r numbers (4). The order of the numbers in the combination matters. For example, 1234 is not the same as 4321.
A combination, on the other hand, represents the number of ways we can select r items from a set of n items when the ordering is not considered. The formula to calculate combinations is:
nCr = (n + r - 1)! / (r! * (n - 1)!)
where n is the total number of items, r is the number of items to select, and ! represents the factorial function.
An example of this is purchising a ticket for a lottery, for most of which the order of the numbers you select does not matter. For example, if you select the numbers 1, 2, 3, 4, 5, 6 for a lottery and they are the numbers picked, you will win the same as if you selected the numbers 6, 1, 4, 2, 3, 5.
Combinatrix is distributed under the MIT License. See the LICENSE file for more details.
Contributions to Combinatrix are welcome! If you encounter any issues or have suggestions for improvements, please open an issue or a pull request on the GitHub repository.