Counting Principle and Permutation Review

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

How many 5-digit (numerical) passwords are possible for the school email system if the first digit cannot be 0 and repetition is NOT allowed?

• 11,424,400

• 10,967,424

• 27,216

• 90,000

There are 17 students in Schnaper's 2nd hour class. How many different seating charts are possible?

• 1

• 17

• 4,080

• 3.6 x 10¹⁴

If a club consists of 10 members, how many different arrangements of president, vice president, and secretary are possible?

• 120

• 720

• 30

• 13

An identification code is to consist of 3 uppercase letters followed by 4 digits. How many different codes are possible if repetition is not permitted?

• 78,624,000

• 175,760,000

• 10,000

• 12

Five different colored flags will be placed on a pole, one beneath another. The arrangement of the colors indicates the message. How many messages are possible if five flags are to be selected from nine different colored flags?

• 45

• 15,120

• 126

• 59,049

How many distinct ways can the letters in the word OPPORTUNITIES be arranged?

• 389,188,800
• 2,028,377,600
• 1,556,755,200
• 16,227,020,800

Homecoming has 7 candidates for King. How many ways can a King and a First Runner-up be chosen to form the Festival Court?

• 23

• 840

• 42

• 3,628,800

In a race in which six automobiles are entered and there are no ties, in how many ways can the first three finishers come in?

• 6

• 120

• 30

• 720

A police department is trying to determine in how many ways they can line up 5 suspects for a witness to view them. Which of the following will NOT give the police the correct total number of ways to line up the suspects?

• 5!

• ₅P₅

• 5x4x3x2x1

• 5x5