1. Permutations Assignment One area where permutations are important is in password protection for computers. You may have heard network administrators encourage people to use “strong” passwords. What makes a password strong?

2. Permutations Assignment Several factors contribute to a strong password. In short, it should be difficult for a hacker to guess what it is. That’s why one guideline is to not use words contained in a dictionary— a dictionary in any language.

3. Permutations Assignment In addition, guidelines usually include a minimum number of characters, as well as a combination of types of characters (lower case, upper case, number, etc.)

4. Permutations Assignment Example: How many passwords are possible if a person uses 3 lower case letters?

5. Permutations Assignment Example: How many passwords are possible if a person uses 3 lower case letters? Using the multiplication principle, each character has 26 possibilities. 26*26*26 = 17,576 possible passwords

6. Permutations Assignment Example: How many passwords are possible if a person uses 3 lower case letters? Working through 17,576 possibilities by hand would be very time consuming, but using a computer program to hack the password would be very simple.

7. Permutations Assignment Example: How many passwords are possible if a person uses 5 letters, combining lower and upper case? Each position now has 52 possibilities, meaning there are 52*52*52*52*52 = 380,204,032 possible passwords—quite an increase compared to the previous example!

8. Permutations Assignment Problem 1: How many passwords are possible if a person uses 8 letters, combining lower and upper case? Problem 2: How many passwords are possible if a person uses 6 characters, including lower and upper case letters and the numbers 0-9?

9. Permutations Assignment Problem 3: How many passwords are possible if a person uses 5 characters, combining lower and upper case letters, the numbers 0-9, and the characters [!,., #, $, %, &, *,,, ?]? Problem 4: How many passwords are possible if a person uses 8 characters, combining lower and upper case letters, the numbers 0-9, and the characters [!,., #, $, %, &, *,,, ?]?

10. Permutations Assignment Problem 5: You are a judge in a talent contest. In how many ways can you rank your top 3 choices among 10 contestants? (Order matters—you will rank them 1 st, 2 nd, and 3 rd.) Problem 6: The talent contest has grown. In how many ways can you rank your top 3 choices among 15 contestants?

11. Permutations Assignment Problem 7: How many routes are possible from Prad to Goze? (Include only routes that visit no city more than once.) Prad Lea Goze

12. Permutations Assignment Problem 8: In the U.S., radio station call letters must begin with either K or W. They must consist of either 3 or 4 letters. With these constraints, how many different radio stations could be assigned call letters? (A letter may be used more than once in a station’s call letters.)

13. Permutations Assignment Problem 9: In the U.S., three-digit area codes started being used in 1947. At that time, the first digit could not be a 0 or 1, the second digit had to be either a 0 or 1, and the third digit could not be 0. How many area codes were possible in 1947?

14. Permutations Assignment Problem 10: To increase the number of available area codes, as of 1995 the second digit could be any number 0- 9. How many area codes were possible starting in 1995? (The previous constraints regarding the first and third digits remain in place.)

15. Permutations Assignment Problem 11: You are taking a True/False quiz with 10 problems. In how many different ways can you complete the quiz? (For example, answering every question True counts as 1 possibility.) (Hint: Remember the multiplication principle!)

16. Permutations Assignment Problem 12: Unfortunately you are ill prepared for the quiz and have decided to totally guess on every problem. What is the probability that you will score 100% on the quiz? (Hint: think about how many ways there are to answer the quiz, and how many answer keys there are.)

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