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 × n.

Front

How many different orders can 6 runners finish a race?

Back

720 (calculated as 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720).

Front

What is a sample space in probability?

Back

A sample space is a list of all possible outcomes of a random experiment.

Front

If you have 1 green, 5 red, 4 blue, and 2 yellow marbles, which combination is NOT possible?

Back

1 Yellow and 2 Green (since there is only 1 green marble).

Front

How many total outcomes are there when rolling a die and flipping a coin?

Back

12 (6 outcomes from the die × 2 outcomes from the coin = 12 total outcomes).

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

How many ways can you choose 3 toppings from 4 options?

Back

There are 4C3 = 4 ways to choose 3 toppings from 4 options.

Front

If you can choose between 4 ice cream flavors and 4 toppings, how many combinations are there?

Back

32 combinations (4 flavors × 4 toppings = 16, then multiplied by 2 for cone or cup).

Front

What is the total number of outcomes when flipping 3 coins?

Back

8 outcomes (2^3 = 8, since each coin has 2 possible outcomes).