Tree Diagrams and Fundamental Counting Principle

Front

What is a tree diagram?

Back

A tree diagram is a visual representation used to show all possible outcomes of a situation, often used in probability and counting problems.

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 two events can occur in m × n ways.

Front

How many different license plates can be made with 2 letters followed by 1 digit?

Back

There are 26 options for each letter and 10 options for the digit. Total = 26 × 26 × 10 = 6760.

Front

How do you calculate the number of combinations when no repetition is allowed?

Back

When no repetition is allowed, multiply the number of choices for each position, decreasing the number of choices for each subsequent position.

Front

If you have 3 letters followed by 3 numbers, how do you calculate the total combinations without repetition?

Back

Total combinations = 26 × 25 × 24 (for letters) × 10 × 9 × 8 (for numbers) = 11232000.

Front

How many different pizzas can you create with 8 meats, 4 cheeses, 3 crust types, and 2 sauces?

Back

Total combinations = 8 × 4 × 3 × 2 = 192.

Front

What is the total number of outfit combinations with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

Back

Total combinations = 5 × 8 × 2 = 80.

Front

What is a combination in counting principles?

Back

A combination is a selection of items where the order does not matter.

Front

What is a permutation in counting principles?

Back

A permutation is an arrangement of items where the order does matter.

Front

How do you find the total number of outcomes in a multi-step experiment?

Back

Multiply the number of outcomes for each step together.