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The lecture covers basic counting rules in discrete mathematics, focusing on the product rule, sum rule, and the pigeonhole principle. It explains how to count distinct arrangements and combinations, as well as apply these rules in various scenarios. Practical examples illustrate the application of these principles, particularly in counting functions and determining valid passwords.
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References
ch33.pdfClass Notes
Memorization
What we have learnt
- Counting is fundamental in ...
- The product rule allows for...
- The sum rule enables counti...
Final Test
Revision Tests
What we have learnt
- Counting is fundamental in discrete mathematics with methodologies for addressing how many of certain objects or arrangements exist.
- The product rule allows for calculating the number of ways to accomplish a set of sequential tasks by multiplying the number of ways to accomplish each subtask.
- The sum rule enables counting distinct outcomes by adding the number of ways to accomplish disjoint tasks.
Key Concepts
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Term: Product Rule
Definition: A counting method used to find the total number of ways to perform tasks that can be broken down into subtasks; if subtasks are independent, the total is the product of the ways to complete each subtask.
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Term: Sum Rule
Definition: A counting method applied to find the total number of ways to complete a task that can be done in different, disjoint ways by summing the number of ways for each way.
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Term: Pigeonhole Principle
Definition: A principle stating that if n items are put into m containers (where n > m), then at least one container must contain more than one item.