Counting Techniques

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 ways can five different books be arranged on a bookshelf?

• 120

• 3125

• 60

• 25

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 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

A human resources director interviews eight people for three identical positions. How many ways can she select three people to move on to the second interview?

• 56

• 336

• 512

• 6561

For summer reading, students must choose one of 5 novels, one of 4 biographies, one of 7 non-fiction books, and one of 6 self-improvement books. How many ways can a student choose 4 books for summer reading?

• 840

• 212,520

• 8855

• 1680

Student council has 24 members. In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?

• 5,100,480

• 0

• 42,504

• 5.17 x 10²¹

Members of 6 different school organizations decorated floats for the homecoming parade.  How many different ways can first, second, and third prize be awarded?

• 18
• 120
• 36