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Generalized pigeonhole principle - PowerPoint PPT Presentation

Chapter 5

Chapter 5

Chapter 5. 5.1 The Basics of Counting 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.4 Binomial Coefficients 5.5 Generalized Permutations and Combinations 5.6 Generating Permutations and Combinations. Basic Counting Principles. Product rule Sum rule.

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22C:19 Discrete Math Counting

22C:19 Discrete Math Counting

22C:19 Discrete Math Counting. Spring 2014 Sukumar Ghosh. The Product Rule. Example of Product Rule. Example of Product Rule. The Sum Rule. Example of Sum Rule. Example of Sum Rule. Wedding picture example. Counting subsets of a finite set.

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657 views • 39 slides
22C:19 Discrete Math Counting

22C:19 Discrete Math Counting

22C:19 Discrete Math Counting. Fall 2011 Sukumar Ghosh. The Product Rule. Example of Product Rule. Example of Product Rule. The Sum Rule. Example of Sum Rule. Example of Sum Rule. Wedding picture example. Counting subsets of a finite set.

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1.36k views • 39 slides
Counting

Counting

Counting. Product Rule. Example. Sum Rule. Pigeonhole principle. If there are more pigeons than pigeonholes, then there must be at least one pigeonhole with at least two pigeons in it

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334 views • 22 slides
Discrete Mathematics Lecture 7

Discrete Mathematics Lecture 7

Discrete Mathematics Lecture 7. Alexander Bukharovich New York University. Generic Functions. A function f: X ? Y is a relationship between elements of X to elements of Y, when each element from X is related to a unique element from Y

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438 views • 20 slides
The Pigeonhole Principle

The Pigeonhole Principle

The Pigeonhole Principle. CS/APMA 202 Rosen section 4.2 Aaron Bloomfield. The pigeonhole principle. Suppose a flock of pigeons fly into a set of pigeonholes to roost If there are more pigeons than pigeonholes, then there must be at least 1 pigeonhole that has more than one pigeon in it

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1.1k views • 14 slides
Review

Review

Review. Previously we determined the number of r-permutations of a set, P(n, r), and we found a formula to calculate P(n, r): And, we determined the number of r-combinations of a set, C(n, r), and we found a formula to calculate C(n, r): And all of this lead to the Binomial Theorem:.

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The Pigeonhole Principle

The Pigeonhole Principle

The Pigeonhole Principle. Section 6. 2. Section Summary. The Pigeonhole Principle The Generalized Pigeonhole Principle. The Pigeonhole Principle. If a flock of 20 pigeons roosts in a set of 19 pigeonholes, one of the pigeonholes must have more than 1 pigeon.

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Turn in HW7 (put your name on it) Return HW6 Avg: 77 Adj Avg: 82.5 Median: 85

Turn in HW7 (put your name on it) Return HW6 Avg: 77 Adj Avg: 82.5 Median: 85

Turn in HW7 (put your name on it) Return HW6 Avg: 77 Adj Avg: 82.5 Median: 85 Emmanuel graded Section 3.1 (green) Pascal graded Section 3.2 (red) http://www.cs.virginia.edu/~cmt5n/cs202/hw6 #24: 8pts, #29: 6pts, #30: 6pts (grouped to 20) Test 2 is Wednesday, April 2

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5.2 The Pigeonhole Principle

5.2 The Pigeonhole Principle

5.2 The Pigeonhole Principle. Theorem 1: The Pigeonhole Principle If k is a positive integer and k+1 or more objects are placed into k boxes, then there is at least one box containing two or more of the objects.

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938 views • 5 slides

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