Permutations Assignment One area where permutations are important is in password protection for...

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?

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.

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.)

Permutations Assignment

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

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

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.

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!

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?

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 [!, ., #, $, %, &, *, ,, ?]?

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 1st, 2nd, and 3rd.)

Problem 6: The talent contest has grown. In how many ways can you rank your top 3 choices among 15 contestants?

Permutations Assignment

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

PradLea

Goze

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.)

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?

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.)

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!)

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.)

Background designs are the property of Geetesh Bajaj. Used with permission. © Copyright, Geetesh Bajaj. All Rights Reserved.