# 25 - Discrete Mathematics Combinations with Repetitions...

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Discrete Mathematics – Combinations with Repetitions 25-1 MIDTERM When: Friday, March 26, regular time 2:30 Where: Here Topics covered: - Relations, Properties of relations - Equivalence relations, and Orders - Cardinality - Functions, Growth of functions - Mathematical induction and Inductive Definitions Midterm will include problems on predicates and quantifiers, sets, and relations

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Introduction Combinations with Repetitions Discrete Mathematics Andrei Bulatov
Discrete Mathematics – Combinations with Repetitions 25-3 Previous Lecture Permutations with repetitions Combinations )! ( ! ! ) , ( r n r n r n C r n - = =

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Discrete Mathematics – Combinations with Repetitions 25-4 Combinations with Repetitions How many ways are there to select four pieces of fruit from a bowl containing apples, oranges, and pears if the order in which the pieces are selected does not matter, only the type of fruit and not the individual piece matter, and there are at least four pieces of each type of fruit in the bowl? Solution (brute force):
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25 - Discrete Mathematics Combinations with Repetitions...

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