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 do both.

Front

How many different combinations of officers can be elected if there are 3 candidates for president, 4 for vice-president, 4 for secretary, and 2 for treasurer?

Back

96 combinations (3 × 4 × 4 × 2 = 96).

Front

If a lock has numbers from 0 to 39, how many different three-digit combinations can be made?

Back

64,000 combinations (40 × 40 × 40 = 64,000).

Front

How many ways can a photo be framed if there are 12 styles of frames, 55 colors, and 11 types of mattes?

Back

7,260 ways (12 × 55 × 11 = 7,260).

Front

What is the format of most North Carolina car license plates?

Back

3 letters followed by 4 digits.

Front

How many different license plates can be made with 3 letters and 4 digits?

Back

175,760,000 plates (26^3 × 10^4 = 175,760,000).

Front

If a quarter is flipped 4 times, how many possible outcomes are there?

Back

16 outcomes (2^4 = 16).

Front

What is the formula to calculate the total number of outcomes when flipping a coin multiple times?

Back

Total outcomes = 2^n, where n is the number of flips.

Front

How do you calculate the number of combinations when choosing from multiple categories?

Back

Multiply the number of choices in each category together.

Front

What is an example of using the Fundamental Counting Principle in real life?

Back

Choosing an outfit: If you have 3 shirts and 2 pairs of pants, you have 3 × 2 = 6 outfit combinations.