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# hw1 - Solutions Homework#1 Chapter 1 Problems 1 Problem 5...

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Solutions - Homework #1 Chapter 1 Problems 1. Problem 5 : For years, telephone area codes in the United States and Canada consisted of a sequence of three digits. The first digit was an integer between 2 and 9; the second digit was either 0 or 1; the third digit was any integer between 1 and 9. How many area codes were possible? How many area codes starting with a 4 were possible? Using the Multiplication Rule for Counting , there are: 8 · 2 · 9 = 144 possible area codes . If the area code must start with a 4, there are: 1 · 2 · 9 = 18 possible . 2. Problem 8c : How many different letter arrangements can be made from the letters MISSISSIPPI? If the 11 letters in “MISSISSIPPI” can be distinguished from each other, there are 11! orderings of these letters. However, since there are 4! ways to arrange the “I”’s, 4! ways to arrange the “S”’s, and 2! ways to arrange the “P”’s for any given permutation so that the same word appears, then there are: 11! 4!4!2! = 34650 different letter arrangements from “MISSISSIPPI.” 3. Problem 10 : In how many ways can 8 people be seated in a row if: (a) there are no restrictions on the seating arrangement. There are 8! = 40320 total permutations of 8 people in a row. (b) persons A and B must sit next to each other. There are: 7 ways to choose 2 adjacent seats for persons A and B, 2 ways to choose which seat A gets & which seat B gets, & 6! ways to seat the remaining 6 people. = 7 · 2 · 6! = 10080 total ways.

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