Section 3.4 Worksheet C (DO NOT WRITE on WORKSHEET)

Section 3.4 Worksheet C (DO NOT WRITE ON WORKSHEET)

1. A landscaper wants to plant 5 oak trees, 4 pine trees and 10 orange trees in a residential neighborhood. If they are spaced evenly, in how many distinguishable ways can they be planted?

2. In how many distinguishable ways can the letters in the word statistics be written?

3. In how many distinguishable ways can the letters in the word abracadabra be written?

4. A landscaper wants to plant 3 orange trees, 4 apple trees, and 3 apricot trees in a neighborhood park. If they are spaced evenly, in how many distinguishable ways can they be planted?

5. Assuming that each character can be either a letter (26 options) or a digit, how many four character license plates are possible?

6. A license plate consists of 1 number, followed by 3 letters, followed by 2 numbers. How many different license plates can be created.

7. A license plate consists of 1 number, followed by 3 letters, followed by 2 numbers. The first digit cannot be smaller than 6 and the last number must be greater than 3. How many different ways can you create a license can be created.

8. Until recently with the advent of cellular phones, modems and pagers the area codes in the United States and Canada followed a certain system. The first number could not be 0 or 1 and the second could only be 0 or 1. Under this system, how many 3 digit area codes are possible?

9. Fifteen cyclists enter a race. In how many ways can they finish in first, second and third place?

10. Five players on a basketball team must choose a player on the opposing team to defend. In how many ways can they choose their defensive assignments?

11. A baseball card collector has six identical Albert Pujols cards and three identical Josh Hamilton cards. The collector s album has nine slots per page in how many distinguishable ways can the collector arrange the nine cards in one page?

12. There are 14 employees at an advertising firm, four will be chosen to present at a New York business conference. How many different ways can the four employees be chosen?

13. In how many distinguishable ways can the letters in the word Massachusetts be written?

14. From a group of 20 people, a jury of 12 people is selected. In how many different ways can a jury of 12 people be selected?

15. In order to conduct an experiment, 5 subjects are randomly selected from a group of 20 subjects. How many different groups of 5 subjects are possible?

16. A pizza shop offers eight toppings. If no topping is used more than once, in how many different ways can a 5 topping pizza be formed?

17. A lottery has 50 numbers. In how many different ways can six of the numbers be selected? (Assume that order of selection is not important.)

18. Four sales representatives for a company are to chosen to participate in a training program. The company has nine sales representatives to choose from. How many different combinations are formed?

19. A UPS driver must deliver in 6 different cities, how many different routes are possible.

20. A UPS driver must deliver in 6 different cities; find the probability that he goes to the six different cities in alphabetical order.

21. The access code to a houses security system consists of four digits. How many different codes are available if the first digit cannot be zero and the arrangement of 3333 is excluded?

22. How many different surveys are required to cover all possible question arrangements if there are 8 questions in a survey?3

23. There are 7 hamsters in a race. How many different ways can they finish in 1st, 2nd, 3rd and 4th place?