Counting Techniques

How many license plates are possible if each contains 3 letters followed by 3 digits if no letters nor digits can be repeated?

• 17,576,000

• 11,232,000

• 312,000

• 2,176,782,336

How many ways can five different books be arranged on a bookshelf?

• 120

• 3125

• 60

• 25

From among 12 projects under consideration, the mayor must put together a prioritized list of 6 projects to submit to the city council for consideration. How many lists can be formed?

• 924

• 665,280

• 479001600

• 72

How many 5-letter arrangements can be made from the letters of the word LOGARITHM?

• 15,120

• 462

• 55

• 181,440

How many ways can you answer a 10 question multiple choice quiz if each question has four options?

• 1,048,576

• 5040

• 10,000

• 210

How many license plates are possible if each contains 3 letters followed by 3 digits if letters and digits can be repeated?

• 17,576,000

• 11,232,000

• 312,000

• 2,176,782,336

How many different five-card hands can be dealt from a standard deck of 52 cards?

• 2,598,960

• 311,875,200

• 260

• 380,204,032

When buying a new car, the customer can choose from 7 different exterior colors, 4 interior colors, and 3 different accessory packages? How many different cars can the customer order?

• 84

• 2184

• 364

• 924

The Pizza Palace at the mall offers two different size pizzas and has 15 topping options. How many different pizzas are possible if no double toppings or half toppings are possible?

• 65,536

• 450

• 256

• 210

At the frozen yogurt shop, there are 12 different toppings you can add to your frozen yogurt. If you can get your yogurt plain or with every topping possible, how many different ways can you get your frozen yogurt?

• 4096

• 144

• 66

• 132