Multiplication Counting Principle

Front

What is the Multiplication Counting Principle?

Back

The Multiplication 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 pizzas can you create with 8 meats, 4 cheeses, 3 crust types, and 2 sauces?

Back

192 different pizzas (8 × 4 × 3 × 2 = 192).

Front

If you can create a 5-digit password with letters A-Z, numbers 0-9, and symbols, how many options are there if the first character is a letter and the last is a symbol, with repetition allowed?

Back

21,323,250 possible passwords.

Front

How many different versions of a car model can be created with 4 trim levels, 5 colors, and 3 interiors?

Back

60 different versions (4 × 5 × 3 = 60).

Front

What is the total number of possible 5-digit passwords if characters cannot be repeated?

Back

146,611,080 possible passwords.

Front

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

Back

Multiply the number of choices in each category together.

Front

What is an example of a scenario where the Multiplication Counting Principle applies?

Back

Choosing an outfit with 3 shirts and 2 pairs of pants: 3 × 2 = 6 combinations.

Front

If a password must start with a letter and end with a symbol, how does this affect the total number of combinations?

Back

It restricts the choices for the first and last characters, but allows for more combinations in the middle.

Front

What is the formula for calculating the number of combinations when repetition is allowed?

Back

n^r, where n is the number of options and r is the number of positions.

Front

How many different passwords can be created if the first character is a letter, the last is a symbol, and the middle three can be anything?

Back

Calculate using the formula: 26 (letters) × 10 (numbers) × 8 (symbols) for the first and last, and 36 (letters + numbers) for the middle.