Section PC.6 Practice Problems

Write answers as whole numbers or simplified fractions unless otherwise noted.

1. A boy owns 5 pairs of pants, 4 shirts, 1 tie, and 3 jackets. How many different outfits can he wear to school if he must wear one of each item?

2. A boy owns 2 pairs of pants, 3 shirts, 8 ties, and 2 jackets. How many different outfits can he wear to school if he must wear one of each item?

3. Bailey has 5 skirts, 9 blouses, and 10 pairs of shoes. How many different skirt-blouse-shoe outfits can she wear?

4. At a restaurant you can choose from 3 appetizers, 8 entrees, and 2 desserts.  How many different three-course meals can you have?

5. A pizza place has pizzas in 4 different sizes, with 12 different flavors for the crust, and 10 different toppings. How many one-topping pizzas can be ordered?

6. Standard automobile license plates in a country display 1 numbers, followed by 2 letters, followed by 4 numbers. How many different standard plates are possible in this system? (Assume repetitions of letters and numbers are allowed.)

7. All of the license plates in a particular state feature three letters followed by three digits (e.g. ABC 123). How many different license plate numbers are available to the state’s Department of Motor Vehicles? (Assume repetitions of letters and numbers are allowed.)

8. 5-letter “words” are formed using the letters A, B, C, D, E, F, G.  How many such words are possible for each of the following conditions?

a. No condition is imposed
b. No letter can be repeated in a word
c. Each word must begin with the letter A. (This is the only condition.)
d. The letter C must be at the end. (This is the only condition.)
e. The second letter must be a vowel. (This is the only condition.)

9. A true-false test contains 13 questions. In how many different ways can this test be completed? (Assume we don’t care about our scores.)

10. A computer password must be eight characters long. How many passwords are possible if only the 26 lowercase letters of the alphabet are allowed? (Assume repetitions of letters are allowed.)

11. A computer password must be ten characters long. How many passwords are possible if numbers, 26 lowercase letters, and 26 uppercase letters are allowed? (Assume repetitions of numbers and letters are allowed).

12. A gate has a standard keypad with the digits 0 through 9. How many possible code combinations are there if the code is 5 digits long. (Assume repetitions of numbers are allowed.)

13. A gate has a standard keypad with the digits 0 through 9. How many possible code combinations are there if the code is 4 digits long. (Assume repetitions of numbers are allowed and the first digit cannot be a zero.)

14. You are taking a quiz that has 11 multiple-choice questions. If each question has 4 possible answers, how many different ways are there to answer the test?

15. How many three-letter “words” can be made from 4 letters “FGHI” if:

a. repetition of letters is allowed
b. repetition of letters is not allowed

16. How many four-letter “words” can be made from 6 letters “AEBWDP” if:

a. repetition of letters is allowed
b. repetition of letters is not allowed

17. How many three-letter “words” can be made from 10 letters “FGHIJKLMNO” if:

a. repetition of letters is allowed
b. repetition of letters is not allowed

18. A pianist plans to play 4 pieces at a recital. In how many ways can she arrange these pieces in the program?

19. In how many different ways can a police department arrange seven suspects in a police lineup if each lineup contains all seven people?

20. A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 15 different colored flags to choose from but only 6 flags will be flown. Find the number of different signals consisting of 6, if the first flag must be brown.

21. A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 7 different colored flags to choose from. Find the number of different signals consisting of 7, if the middle flag must be brown, the ends must be yellow or pink.

22. In how many ways can first, second, and third prizes be awarded in a contest with 210 contestants? (Assume a contestant can only win one prize.)

23. Seven Olympic sprinters are eligible to compete in the 4 x 100-meter relay race for the USA Olympic team. How many four-person relay teams can be selected from among the seven athletes?

24. A computer user has downloaded 25 songs using an online file-sharing program and wants to create a CD-R with ten songs to use in his portable CD player. If the order that the songs are placed on the CD-R is important to him, how many different CD-Rs could he make from the 25 songs available to him?

25. In how many ways can you choose a President, secretary, and treasurer for a club from 12 candidates, if each candidate is eligible for each position, but no candidate can hold 2 positions?

26. In how many distinct ways can the letters of the word “CLASSROOMS” be arranged?

27. In how many distinct ways can the letters of the word “ACCOMMODATION” be arranged?

28. In how many distinct ways can the letters of the word “COPYRIGHTED” be arranged?

29. In how many distinct ways can the digits in the number 354,883,111 be arranged?

30. A signal can be sent from one location to another by running colored flags up a flagpole, one above the other. There are 15 colored flags to choose from, 3 white, 4 blue, and 2 green, and 6 yellow.  Find the number of different signals consisting of 15 flags.