For the decision algorithms, find how many outcomes are...

For the decision algorithms, find how many outcomes are possible.
$\begin{array}{ll}\text { Step 1: } & \text { Step 2: } 5 \text { outcomes }\end{array}$ Alternative $1:$ Step $1: 3$ outcomes Step 2: 1 outcome Alternative $2: 2$ outcomes

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Key Concepts

Decision Algorithms

Decision algorithms are procedures that guide choices through a sequence of steps, often visualized as a decision tree, where each branch represents a decision point with associated outcomes. Analyzing these algorithms involves counting possible outcomes at each stage and combining these using the appropriate counting principles, such as the multiplication or addition principle, to understand the overall decision structure.

Fundamental Counting Principle

The fundamental counting principle is a basic concept in combinatorics that allows you to calculate the total number of outcomes by multiplying the number of ways each independent step or event can occur. When a process is broken down into a sequence of steps, where each step has a certain number of possibilities, this principle provides a straightforward method for obtaining the overall number of outcomes.

Addition Principle

The addition principle is used when a process can follow several mutually exclusive alternatives or paths. It states that if you have different scenarios that cannot occur simultaneously, the total number of outcomes is the sum of the outcomes for each scenario. This principle is crucial when evaluating decision algorithms that have separate branches, each with its own set of outcomes.

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