- #[[MA284 - Discrete Mathematics]]
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- **Next topic:** [[Principle of Inclusion-Exclusion]]
- **Relevant Slides:** ![Week01.pdf](../assets/Week01_1662844828934_0.pdf)
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- What is **Combinatorics**? #card
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	- **Combinatorics** is the mathematics of *counting*.
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- ## The Additive & Multiplicative Principles
	- ### The Additive Principle
		- What is the **Additive Principle**? #card
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			- If an event $A$ can occur $m$ ways, and event $B$ can occur $n$ (disjoint) ways, then event "$A$ **or** $B$" can occur $m + n$ ways.
	- ### The Multiplicative Principle
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		- What is the **Multiplicative Principle**? #card
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			- If event $A$ can occur $m$ ways, and each possibility allows for event $B$ to occur in $n$ (disjoint) ways, then the event "$A$ **and** $B$" can occur in $m \times n$ ways.
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- ## Counting with Sets
	- What is a **set**? #card
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		- A **set** is a collection of things.
		- The items in a set are called *elements*.
		- A set is **unordered** and does not contain duplicates. i.e.:
			- $$\{a,b,c\} = \{b,a,c\} = \{a,a, c,b,b,b\}$$