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The most basic ideas in combinatorics include: factorials The number of possible arrangements of distinct items is n-factorial, written , which equals * Example: Three items, A, B, and C, can be arranged in different ways: ABC, ACB, BAC, BCA, CAB, and CBA. permutations The number of arrangements that are possible when a subset of items is taken from a set of distinct items is a "permutation of objects taken at a time", which can be written as or , and is equal to . * Example: The number of possible arrangements of the four letters A, B, C, D, taken two at a time, is : AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, and DC. combinations The number of possible subsets of items taken from a set of items, where the order of the items doesn't matter (e.g., the sets ABC a

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  • Combinatorics
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  • The most basic ideas in combinatorics include: factorials The number of possible arrangements of distinct items is n-factorial, written , which equals * Example: Three items, A, B, and C, can be arranged in different ways: ABC, ACB, BAC, BCA, CAB, and CBA. permutations The number of arrangements that are possible when a subset of items is taken from a set of distinct items is a "permutation of objects taken at a time", which can be written as or , and is equal to . * Example: The number of possible arrangements of the four letters A, B, C, D, taken two at a time, is : AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, and DC. combinations The number of possible subsets of items taken from a set of items, where the order of the items doesn't matter (e.g., the sets ABC a
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abstract
  • The most basic ideas in combinatorics include: factorials The number of possible arrangements of distinct items is n-factorial, written , which equals * Example: Three items, A, B, and C, can be arranged in different ways: ABC, ACB, BAC, BCA, CAB, and CBA. permutations The number of arrangements that are possible when a subset of items is taken from a set of distinct items is a "permutation of objects taken at a time", which can be written as or , and is equal to . * Example: The number of possible arrangements of the four letters A, B, C, D, taken two at a time, is : AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, and DC. combinations The number of possible subsets of items taken from a set of items, where the order of the items doesn't matter (e.g., the sets ABC and BCA are considered equivalent), is a "combination of objects taken at a time", which is written or or , and is equal to . * Example: The number of subsets of two letters chosen from the four letters A, B, C, and D, is : AB, AC, AD, BC, BD, and CD. distributions partitions of integers or of sets recurrence relations inclusions inversions inclusion/exclusion principle derangements and subfactorials repetitions and replacements various restrictions placed on problems fundamental counting principle circular permutations generating functions free and fixed permutations, rotational symmetry and reflective symmetry cyclic permutations multisets Pascal's Triangle
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