Counting principle

Learning Objectives Define key terms such as outcome, event, and sample space. Explain the Fundamental Counting Principle in their own words. Apply the Fundamental Counting Principle to determine the total number of outcomes for a sequence of events. Construct a tree diagram to visualize and count all possible outcomes for simple scenarios. Solve multi-step problems involving counting, including those with specific restrictions. Differentiate between situations requiring multiplication (AND) and those requiring addition (OR). How many different outfits can you make with 3 shirts and 2 pairs of pants? 👕👖 Let's find out without drawing every single one! This lesson introduces the Fundamental Counting Principle, a powerful shortcut for finding the total number of possib...

TermDefinitionExample OutcomeA single possible result of an experiment or trial.When rolling a standard six-sided die, rolling a '4' is one possible outcome. EventA specific set of one or more outcomes. An event can be a single outcome or a group of outcomes.When rolling a standard six-sided die, the event 'rolling an even number' consists of the outcomes {2, 4, 6}. Sample SpaceThe set of all possible outcomes of an experiment.The sample space for flipping a coin is {Heads, Tails}. The sample space for rolling a six-sided die is {1, 2, 3, 4, 5, 6}. Tree DiagramA diagram that shows all the possible outcomes of an event or series of events. Each branch represents a possible outcome.To show the outcomes of flipping a coin twice, the first set of branches would be 'He...

The Fundamental Counting Principle (Multiplication Rule) If there are m_1 ways for the first event to occur, m_2 ways for the second event to occur, ..., and m_k ways for the k-th event to occur, then the total number of ways for the sequence of events to occur is m_1 \times m_2 \times ... \times m_k. Use this rule when a task or choice is made up of a sequence of smaller choices or stages, and you want to find the total number of combinations. Think of it as the 'AND' rule: you make choice 1 AND choice 2 AND so on. The Addition Rule (for Disjoint Events) If there are m ways to do one task and n ways to do another task, and the tasks cannot be done at the same time, then there are m + n ways to choose one of these tasks. Use this rule when you have to make a single...