Tree Diagrams and Fundamental Counting Principle

Front

What is a tree diagram?

Back

A tree diagram is a visual representation that shows all possible outcomes of an event, branching out from a starting point.

Front

What does the fundamental counting principle state?

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 outcomes for both events is m × n.

Front

How many different outcomes are there for 2 letters followed by 1 digit?

Back

There are 6760 different outcomes for 2 letters (26 options each) and 1 digit (10 options): 26 × 26 × 10 = 6760.

Front

If a cafeteria serves 3 types of sandwiches and 2 types of drinks, how many combinations can be made?

Back

There are 6 combinations: 3 sandwiches × 2 drinks = 6 combinations.

Front

How many outfits can be made with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

Back

80 outfits can be made: 5 × 8 × 2 = 80.

Front

What is the total number of outcomes for 3 sandwiches and 2 drinks?

Back

The total number of outcomes is 6: 3 sandwiches × 2 drinks = 6.

Front

What is an example of a tree diagram?

Back

An example of a tree diagram is showing the outcomes of flipping a coin twice: HH, HT, TH, TT.

Front

How do you calculate the total outcomes for multiple events?

Back

Multiply the number of outcomes for each event together.

Front

What is the formula for the fundamental counting principle?

Back

The formula is: Total Outcomes = m × n, where m is the number of ways for the first event and n is the number of ways for the second event.

Front

If you have 4 shirts and 3 pants, how many outfits can you create?

Back

You can create 12 outfits: 4 shirts × 3 pants = 12.