9.1 Basic Combinatorics

To buy a computer system, a customer can choose one of 4 monitors, one of 2 keyboards, one of 4 computers and one of 3 printers. Determine the number of possible systems that a customer can choose from.

• 128

• 8

• 32

• 96

A student can select one of 6 different mathematics books, one of 3 different books and one of 4 different science books. In how many way can a student select a book of mathematics, a book of chemistry and book of science?

• 27

• 72

• 54

• 68

There are 3 different roads from City A to City B and 2 different roads from City B to City C. In how many ways can someone go from City A to City C by passing through City B?

• 2

• 3

• 6

• 12

A man has 3 different suits, 4 different shirts and 5 different pairs of shoes. In how many different ways can this man wear a suit. a shirt and a pair of shoes?

• 12

• 24

• 48

• 60

In a certain country telephone numbers have 9 digits. The first two digits are the area code (03) and are the same within the given area. The last 7 digits are the local number and cannot begin with 0. How many different telephone numbers are possible within a given area code in this country?

• 9,000,000

• 10,000,000

• 3,000,000

• 90,000,000

How many different ways can 3 students line up to purchase a new textbook ?

• 0

• 1

• 2

• 6

In one game, a code made using different colors is created by one player (the codemaker), and the other player (the codebreaker) tries to guess the code. The codemaker gives hints about whether the colors are correct and in the right position.

The possible colors are Blue, Yellow, White, Red, Orange, and Green. How many 4-color codes can be made if the colors cannot be repeated?

• 720

• 360

• 120

• 24

A club of 9 people wants to choose a board of three officers: President, Vice President, and Secretary. How many ways are there to choose the board from the 9 people?

• 900

• 810

• 702

• 504

There are 12 horses in a horse show competition. The top three winning horses receive money. How many possible money winning orders are there for a competition with 12 horses?

• 36

• 120

• 1200

• 1320

Fred is lining up his four golf trophies on a shelf. How many different possible arrangements can he make?

• 24

• 16

• 10

• 4