Counting principle

Learning Objectives Define the Fundamental Counting Principle and distinguish it from the Addition Principle. Apply the Multiplication Rule to calculate the total number of outcomes for a sequence of independent events. Apply the Addition Rule to calculate the total number of outcomes for mutually exclusive events. Distinguish between problems that require repetition and those that do not. Solve multi-step counting problems by combining the Addition and Multiplication Principles. Model and solve real-world scenarios involving choices and arrangements, such as passwords, license plates, or outfits. Construct and interpret tree diagrams for simple counting problems. How many different outfits can you make with 3 shirts, 2 pairs of pants, and 2 pairs of shoes? 👕👖👟 Let&#039...

TermDefinitionExample OutcomeA single possible result of an experiment or trial.When rolling a standard six-sided die, rolling a '4' is one possible outcome. Sample SpaceThe set of all possible outcomes of an experiment.The sample space for flipping a coin is {Heads, Tails}. EventA specific outcome or a set of outcomes. Events can be simple (one outcome) or compound (multiple outcomes).When drawing a card from a standard deck, drawing the 'King of Hearts' is a simple event. Drawing 'any King' is a compound event. Independent EventsTwo or more events where the outcome of one event does not affect the outcome of the other(s).Flipping a coin and rolling a die. The result of the coin flip has no impact on the result of the die roll. Mutually Exclusive EventsTwo o...

The Multiplication Principle (Fundamental Counting Principle) If event A can occur in 'm' ways and event B can occur in 'n' ways, then the number of ways that both A and B can occur is m \times n. Use this rule for 'AND' situations, where you are making a sequence of choices or performing a series of tasks one after another. The events must be independent. The Addition Principle If event A can occur in 'm' ways and event B can occur in 'n' ways, and A and B are mutually exclusive, then the number of ways that either A or B can occur is m + n. Use this rule for 'OR' situations, where you are choosing between two or more distinct options that cannot happen at the same time.