Tree Diagrams and Fundamental Counting Principle

Front

What is a tree diagram?

Back

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

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 do you calculate the total number of outfits from multiple clothing options?

Back

Multiply the number of options for each clothing type. For example, with 5 jeans, 8 t-shirts, and 2 shoes: 5 × 8 × 2 = 80 outfits.

Front

What is the formula for calculating permutations without repetition?

Back

For 'n' items taken 'r' at a time, the formula is n! / (n - r)!.

Front

How many different license plates can be formed with 3 letters followed by 3 numbers without repetition?

Back

26 x 25 x 24 x 10 x 9 x 8 = 11,232,000.

Front

How do you find the number of combinations for a menu with multiple choices?

Back

Multiply the number of choices for each category. For example, 6 sandwiches, 3 chips, and 5 beverages: 6 × 3 × 5 = 90 combinations.

Front

What is the total number of choices when selecting a cone and ice cream flavor?

Back

Multiply the number of cone types by the number of ice cream flavors. For 3 cones and 31 flavors: 3 × 31 = 93 choices.

Front

How do you calculate the number of passwords with repeated letters?

Back

If there are 'n' letters and 'r' positions, the formula is n^r. For 4 letters in 4 positions: 4^4 = 256.

Front

What is the difference between combinations and permutations?

Back

Combinations are selections where order does not matter, while permutations are arrangements where order does matter.

Front

How do you represent a situation with multiple independent choices?

Back

Use a tree diagram to visualize each choice and its possible outcomes.