6 patterns of combinations and permutations
We will introduce the pattern generation page for combinations and permutations. Please use it to actually check the image visually.
Combination
A combination represents the number of ways to select some element from a set. It is characterized by the fact that it does not take into account the order, for example, to calculate the pattern when choosing 2 people out of 5 people.
Combination with Repetition
Duplicate combinations are combinations in which the same element can be selected more than once. For example, if you choose two of three different fruits, you can also choose two of the same fruit.
(Partial) Permutation
(partial) Permutations refer to the number of ways to pick some elements from a set and arrange them in order. Refers to a permutation when the number of elements to be selected is less than the number of elements in the set. The reason why we use (partial) here is that we are not necessarily singleing out all elements.
Permutation with Repetition
A duplicate permutation is a permutation in which the same element can be used repeatedly. For example, if you have a set of two elements, ‘A’ and ‘B’, and you repeatedly use each element to create a permutation of three elements, there are eight ways: AAA, AAB, ABA, ABB, BAA, BAB, BBB.
Circular Permutation
A circle permutation is a permutation of elements on a circle. Since the starting point is not fixed, a different calculation method is required than the usual permutation.
Necklace Permutation
A rosary permutation is a type of circular permutation that takes into account rotation and inversion. It was named because it has a shape with a series of elements like a rosary. Since the right or left direction of the circle permutation does not matter, the number of patterns is halved.
This concludes the Combination and Permutation Generation page. Please bookmark it and use it.
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