Counting Principle, Permutations and Combinations

A team of 8 basketball players needs to choose a captain and co-captain.

• 64
• 56
• 15
• 40,320

A group of 25 people are going to run a race. The top 8 finishers advance to the finals.

• 200
• 4.3609 x 10¹⁰
• 0
• 1,081,575

A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many possible combinations of pizza with one topping are there? 

• 64
• 14
• 24,024
• 2184

You go to Best Buy to purchase a new television. You have the following choices: LCD or plasma; screen size 27”, 32”, 36”, 41”, 51”, or 63” and manufacturer Sony, Vizio or Phillips. How many different televisions does the store have to offer? 

• 18
• 990
• 72
• 36

A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals.

• 135
• 85,140
• 14,190
• 91,125

5 out of 13 students will ride in a car instead of a van

• 1,287
• 154,440
• 371,293
• 65

There are 45 applicants for three Computer Programmer positions.

• 135
• 85,140
• 14,190
• 91,125

A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there?

• 40
• 5040
• 6561
• 10,000

A lock has four dials. On each dial are the digits 0 to 9. How many possible combinations are there if you cannot reuse a number?

• 40
• 5040
• 6561
• 10,000

When does the order in which you are choose matter?

• Combination
• Permutation