Fundamental Counting Principle

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the total number of ways both events can occur is m x n.

Front

How many license plate numbers consisting of three letters followed by three numbers are possible when repetition is allowed?

Back

26 x 26 x 26 x 10 x 10 x 10 = 17,576,000

Front

If Jared can choose from high-top or low-top, shoelaces or velcro, and the colors black, white, and red, how many styles of sneakers are possible?

Back

12 styles (2 choices for type x 2 choices for laces x 3 colors = 12)

Front

What is the total number of outcomes for picking a day of the week and a month of the year?

Back

84 outcomes (7 days x 12 months = 84)

Front

How can shoppers in a mall be categorized based on gender, age, and payment method?

Back

8 ways (2 genders x 2 age groups x 2 payment methods = 8)

Front

What is the total number of outcomes for picking a cat or dog and choosing the colors black, brown, or spotted?

Back

6 outcomes (2 animals x 3 colors = 6)

Front

What is the formula for calculating the total outcomes when multiple choices are involved?

Back

Total outcomes = (number of choices for event 1) x (number of choices for event 2) x ...

Front

Define 'independent events' in the context of counting principles.

Back

Independent events are events where the outcome of one event does not affect the outcome of another.

Front

What is the significance of repetition in counting problems?

Back

Repetition allows for the same choice to be made multiple times, increasing the total number of outcomes.

Front

How does the counting principle apply to combinations of different categories?

Back

The counting principle can be applied by multiplying the number of choices in each category to find the total combinations.