Counting Principle
A lunch menu consists of 8 different kinds of sandwiches, 3 different kinds of soup, and 12 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink?
288 different choice
How many different four-letter arrangements can be made from the letters in the word “CHAIRS,” if the same letter may be used only once?
360 different 4-letter arrangements
Alexa wants to order a two-topping pizza from the local pizzeria. If there is 18 different toppings to choose from, then how many different pizzas can she order?
153 different 2-topping pizzas
A math club has 30 boys and 20 girls. How many different 5-member teams can be form if the team must consisting of 3 boys and 2 girls?
771,400 different 5-member teams
Jamestown Builders has a development of new homes. There are 6 different floor plans, 20 exterior colors, and an option of either a one- or a two-car garage. How many choices are there for one home?
240 different choices for a home
The Mathematics Club will select a president, a vice president, and a treasurer for the club. If there are 38 members in the club, how many different selections of a president, a vice president, and a treasurer are possible if each club member can be selected to only one position?
50,616 different selections of the three positions
If the Math Olympiad Club consists of 14 students, how many different teams of 6 students can be formed for competitions?
3,003 math teams
In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 14 boys and 8 girls are competing, how many different ways could the six medals possibly be given out?
733,824 different results of the running competition
How many ways can you answer a 7-question True/False test?
128 different ways
6,227,020,800 possible race results
three cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of three cards are possible?
22,100 different sets
On a bookshelf, there are five different mystery books and six different biographies. How many different sets of four books can Emilio choose if two of the books must be mystery books and two of the books must be biographies?
150 different sets of 4 books
How many different 5-digit odd numbers are possible if digits may be repeated?
45,000 different 5-digit odd numbers
A lock has a 3-number code that is selected using the numbers 0 through 35. If none of the numbers are allowed to repeat, how many different lock codes are there?
42,840 lock codes
Ms. Bell's mathematics class consists of 12 sophomores, 15 juniors, and 7 seniors. How many different ways can Ms. Bell create a 5-member committee of sophomores if each sophomore has an equal chance of being selected?
792 5-member committee of just sophomores
Megan decides to go out to eat. The menu at the restaurant has four appetizers, three soups, seven entrees, and five desserts. If Megan decides to order an appetizer or a soup, and one entree, and two different desserts, how many different choices can she make?
490 choices can be made