Fundamental Counting Principle

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to perform both actions.

Front

If a customer can choose from 3 types of cones and 31 flavors of ice cream, how many different combinations can they make?

Back

93 combinations (3 cones × 31 flavors = 93).

Front

How many meal combinations can be made with 2 salads, 3 entrees, and 2 beverages?

Back

12 combinations (2 salads × 3 entrees × 2 beverages = 12).

Front

What is a tree diagram?

Back

A tree diagram is a visual representation that shows all possible outcomes of an event, helping to organize and count outcomes systematically.

Front

How many ways can a coach arrange a batting order for 10 players?

Back

3628800 ways (10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3628800).

Front

What is the formula for calculating permutations of 'n' items taken 'r' at a time?

Back

The formula is P(n, r) = n! / (n - r)!.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.

Front

If there are 4 shirts and 3 pairs of pants, how many outfits can be made?

Back

12 outfits (4 shirts × 3 pants = 12).

Front

What is the total number of outcomes when flipping a coin 3 times?

Back

8 outcomes (2^3 = 8).

Front

How do you calculate the total outcomes for multiple independent events?

Back

Multiply the number of outcomes for each event together.