23a-Permutations

23a-Permutations - Introduction Permutations Discrete...

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Permutations Discrete Mathematics
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Discrete Mathematics - Permutations 22-2 Previous Lecture Combinatorics Rule of Sum Rule of Product
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Example: In how many ways can we select 3 students from a group of 5 student to stand in a line for a picture? Solution: First, note that the order in which we select students matters. There are 5 ways to select the first student. Once the first one is selected we are left with 4 ways to select the second student. After selecting the first 2 students there are 3 ways to select the third one. By the rule of product, there are 5 4 3 = 60 ways to select students. Discrete Mathematics - Permutations 23-3 Permutations
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Discrete Mathematics - Permutations 23-4 Permutations Given a collection of n distinct objects, any (linear) arrangement of these objects is called a permutation of the collection. A permutation of size r (0 r n) is any (linear) arrangement of r distinct objects from the collection
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Discrete Mathematics - Permutations 23-5 The Number of Permutations Similar to the example on the previous slide, the number P(n,r) of permutations of size r from a collection of n objects can be found as follows: We choose r elements out of n and the order matters.
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23a-Permutations - Introduction Permutations Discrete...

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