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24 - Introduction Combinations Discrete Mathematics Andrei...

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Introduction Combinations Discrete Mathematics Andrei Bulatov
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Discrete Mathematics – Combinations 24-2 Previous Lecture Rule of Sum Rule of Product Permutations
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Discrete Mathematics – Combinations 24-3 Permutations with Repetitions How many different 4-letter words (not necessarily meaningful) can be built permuting the letters of the word COOL? If all letters were distinct then the answer would be the number of all permutations of a 4-element set. However, in words we build we do not distinguish two O. So, words are equal. For each of the words we are interested in, there are two words in which the two O’s are distinguished. Therefore the answer is 1 2 2 1 CLO O and CLO O 12 2 ! 4 =
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Discrete Mathematics – Combinations 24-4 Permutations with Repetitions (cntd) Theorem . If there are n objects with indistinguishable objects of a first type, indistinguishable objects of a second type, … , and indistinguishable objects of a type r, where , then there are (linear) arrangements of the given n objects.
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