Sequential Counting Technique

11.. In a different plan for area codes, the first digit could be any number from through 8the second digit was either 3,4,5, or 6and the third digit could be any number except 4,8, or 9With this plan, how many different area codes are possible?


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12. License plates in a particular state display 4 letters followed by 2 numbers. How many different license plates can be manufactured for this state?

13. How many different arrangements of 4 letters can be formed if the first letter must be W or K (repeats of letters are allowed)?

14. A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 4 stocks?

19. How many five-digit odnumbers are possible if the leftmost digit cannot be zero?

20. In order to develop a more appealing cheeseburger, a franchise uses taste tests with 1different buns, 7 different cheeses, 3 types of lettuce, and 3 types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?

21. If there are 4 math courses, 3 psychology courses, and 5 English courses offered in non-overlapping times so that you could select one of each for your schedule, how many different schedules would be possible?

22. There are three sizes of pizza, three types of crust, and ten toppings. If you order one size, one type of crust, and one topping, how many pizza choices are there?

23. You won the lottery!! You decide to first buy the expensive car you’ve always loved. There are lots of options. In addition to deciding whether you want an automatic or manual transmission, you have to choose an exterior color from 15 options, an interior color from 12 options, seats that have either a heating or massage option, 4 different types of audio systems, and 5 luxury packages with special extras for your car. If you pick one in each category, how many different car packages are there?

24. You are taking an online survey. There are 10 questions with each question having 4 choices. In how many ways can you answer the questions if you leave no questions blank?

25. Solve the problem by applying the Fundamental Counting Principle. A restaurant offers entrees and 8 desserts. In how many ways can a person order a two-course meal?

26. Solve the problem by applying the Fundamental Counting Principle. A restaurant offers a choice of salads, 6 main courses, and 3 desserts. How many possible 3coursmeals are there?

27. Solve the problem by applying the Fundamental Counting Principle. There are roads leading from Bluffton to Hardeeville, 8 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon?

28. Solve the problem by applying the Fundamental Counting Principle. An apartment complex offers apartments with four different options, designated by A through D.

A=number of bedrooms (one through four)

B=number of bathrooms (one through three)

C=floor (first through fifth)

D=outdoor additions (balcony or no balcony)

How many apartment options are available?

29. Solve the problem by applying the Fundamental Counting Principle. You are taking a multiple-choice test that has questions. Each of the questions has 4 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?

30. Solve the problem by applying the Fundamental Counting Principle. License plates in a particular state display letters followed by 3 numbers. How many different license plates can be manufactured? (Repetitions are allowed.)

31. Solve the problem by applying the Fundamental Counting Principle. How many different four-letter secret codes can be formed if the first letter must be an S or a T? (Repetition is allowed.)

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