Section 4.2 Counting
259
exeRciSeS 4.2
1. A frozen yogurt shop allows you to choose one flavor (vanilla, strawberry, lemon, cherry, or peach),
one topping (chocolate shavings, crushed toffee, or crushed peanut brittle), and one condiment (whipped
cream or shredded coconut). How many different desserts are possible?
2. In Exercise 1, how many dessert choices do you have if you are allergic to strawberries and chocolate?
3. A video game is begun by making selections from each of 3 menus. The first menu (number of players)
has 4 selections, the second menu (level of play) has 8, and the third menu (speed) has 6. In how many
configurations can the game be played?
4. A multiple choice exam has 20 questions each with 4 possible answers and 10 additional questions each
with 5 possible answers. How many different answer sheets are possible?
5. A user’s password to access a computer system consists of 3 letters followed by 2 digits. How many different passwords are possible?
6. On the computer system of Exercise 5, how many passwords are possible if uppercase and lowercase letters can be distinguished?
7. A telephone conference call is being placed from Central City to Booneville by way of Cloverdale. There
are 45 trunk lines from Central City to Cloverdale and 13 from Cloverdale to Booneville. How many different ways can the call be placed?
8. A, B, C, and D are nodes on a computer network. There are 2 paths between A and C, 2 between B and
D, 3 between A and B, and 4 between C and D. Along how many routes can a message from A to D
be sent?
9. How many nine-digit Social Security numbers are possible?
10. An apartment building purchases a new lock system for its 175 units. A lock is opened by punching in a
two-digit code. Has the apartment management made a wise purchase?
11. A palindrome is a string of characters that reads the same forward and backward. How many five-letter
English language palindromes are possible?
12. How many three-digit numbers less than 600 can be made using the digits 8, 6, 4, and 2?
13. A binary logical connective can be defined by giving its truth table. How many different binary logical
connectives are there?
14. Three seats on the county council are to be filled, each with someone from a different party. There are 4
candidates running from the Concerned Environmentalist party, 3 from the Limited Development party,
and 2 from the Friends of the Spotted Newt party. In how many ways can the seats be filled?
15. In the original BASIC programming language, an identifier must be either a single letter or a letter
followed by a single digit. How many identifiers are possible?
16. A president and vice-president must be chosen for the executive committee of an organization. There are
17 volunteers from the Eastern Division and 24 volunteers from the Western Division. If both officers
must come from the same division, in how many ways can the officers be selected?
17. A dinner special allows you to select from 5 appetizers, 3 salads, 4 entrees, and 3 beverages. How many
different dinners are there?
18. In Exercise 17, how many different dinners are there if you may have an appetizer or a salad but not both?
19. A new car can be ordered with a choice of 10 exterior colors; 7 interior colors; automatic or three-speed
or five-speed transmission; with or without air conditioning; with or without power steering; and with or
without the option package that contains the power door lock and the rear-window defroster. How many
different cars can be ordered?
20. In Exercise 19, how many different cars can be ordered if the option package comes only on a car with an
automatic transmission?
259
exeRciSeS 4.2
1. A frozen yogurt shop allows you to choose one flavor (vanilla, strawberry, lemon, cherry, or peach),
one topping (chocolate shavings, crushed toffee, or crushed peanut brittle), and one condiment (whipped
cream or shredded coconut). How many different desserts are possible?
2. In Exercise 1, how many dessert choices do you have if you are allergic to strawberries and chocolate?
3. A video game is begun by making selections from each of 3 menus. The first menu (number of players)
has 4 selections, the second menu (level of play) has 8, and the third menu (speed) has 6. In how many
configurations can the game be played?
4. A multiple choice exam has 20 questions each with 4 possible answers and 10 additional questions each
with 5 possible answers. How many different answer sheets are possible?
5. A user’s password to access a computer system consists of 3 letters followed by 2 digits. How many different passwords are possible?
6. On the computer system of Exercise 5, how many passwords are possible if uppercase and lowercase letters can be distinguished?
7. A telephone conference call is being placed from Central City to Booneville by way of Cloverdale. There
are 45 trunk lines from Central City to Cloverdale and 13 from Cloverdale to Booneville. How many different ways can the call be placed?
8. A, B, C, and D are nodes on a computer network. There are 2 paths between A and C, 2 between B and
D, 3 between A and B, and 4 between C and D. Along how many routes can a message from A to D
be sent?
9. How many nine-digit Social Security numbers are possible?
10. An apartment building purchases a new lock system for its 175 units. A lock is opened by punching in a
two-digit code. Has the apartment management made a wise purchase?
11. A palindrome is a string of characters that reads the same forward and backward. How many five-letter
English language palindromes are possible?
12. How many three-digit numbers less than 600 can be made using the digits 8, 6, 4, and 2?
13. A binary logical connective can be defined by giving its truth table. How many different binary logical
connectives are there?
14. Three seats on the county council are to be filled, each with someone from a different party. There are 4
candidates running from the Concerned Environmentalist party, 3 from the Limited Development party,
and 2 from the Friends of the Spotted Newt party. In how many ways can the seats be filled?
15. In the original BASIC programming language, an identifier must be either a single letter or a letter
followed by a single digit. How many identifiers are possible?
16. A president and vice-president must be chosen for the executive committee of an organization. There are
17 volunteers from the Eastern Division and 24 volunteers from the Western Division. If both officers
must come from the same division, in how many ways can the officers be selected?
17. A dinner special allows you to select from 5 appetizers, 3 salads, 4 entrees, and 3 beverages. How many
different dinners are there?
18. In Exercise 17, how many different dinners are there if you may have an appetizer or a salad but not both?
19. A new car can be ordered with a choice of 10 exterior colors; 7 interior colors; automatic or three-speed
or five-speed transmission; with or without air conditioning; with or without power steering; and with or
without the option package that contains the power door lock and the rear-window defroster. How many
different cars can be ordered?
20. In Exercise 19, how many different cars can be ordered if the option package comes only on a car with an
automatic transmission?