Fundamental Counting Principle & Factorials

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15
• 40
• 80
• 10

A particular model at a New Car Dealership comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

• 180
• 23
• 12
• 60

How many license plates consisting of three letters followed by three numbers are possible when no repetition is allowed?

• 26 x 25 x 24 x 10 x 9 x 8 = 11232000

• 26 x 26 x 26 x 10 x 10 x 10 = 17576000

• 26 x 25 x 24 x 9 x 8 x 7 = 7862400

• 26 x 26 x 26 x 9 x 9 x 9 = 12812904

A menu has 6 different sandwiches, with 3 choices of potato chips, 3 types of salad and 5 different beverages. How many different lunch combinations consisting of a sandwich, chips and beverage can be ordered?

• 30
• 17
• 90
• 270

The letters A, B, C, and D are used to form four-letter passwords for entering a computer file. How many passwords are possible if letters can be repeated?

• 4 x 4 x 4 x 4 = 256

• 4 x 3 x 2 x 1 = 24

• 4 + 4 + 4 + 4 = 16

• 4 + 3 + 2 + 1 = 10

The Palace of Pizza offers small, medium, or large pizzas with 14 different toppings available. How many different 1-topping pizzas do they serve?

• 3 x 14 = 42

• 3 + 14 = 17

• 14 x 14 x 14 = 2744

• 14 x 13 x 12 = 2184

In Cornville, bicycle license plates have 2 letters followed by a 1-digit number. How many different license plates are possible?

• 6760

• 62

• 2600

• 6084

Use the fundamental counting principle to find the total number of possible outcomes for my smartphone lock screen if I have to use 4 different numbers from 0-9, and I can reuse numbers. (For instance, I could use "1111")

• 6,561, because 9 x 9 x 9 x 9 = 6,561

• 5,040, because 10 x 9 x 8 x 7 = 5,040

• 10,000, because 10 x 10 x 10 x 10 = 10,000

• 1111, because that's the number in the problem.

Using the fundamental counting principle, how many different possible codes are there to lock my iPhone if I use 4 digits, each digit has to be a number from 0-9, and I cannot use the same number twice? (For instance, I could use codes like 1234)

• 5,040, because 10 x 9 x 8 x 7 = 5,040

• 1234, because that's the number in the problem

• 10,000 because 10 x 10 x 10 x 10 = 10,000

• 40, because 10 + 10 + 10 + 10 = 40

At Papa John's you are deciding on what you want for dinner. The pizza offers 8 different meats, 4 different cheeses, 3 different crust types and 2 different sauces. How many different pizzas do you have to choose from?

• 32
• 192
• 40,320
• 51,200