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Math 1320 Quiz Name:__________________________________________ ID number:______________ Instructions: Solve the following problems. Show all your work in order to get full credit. Problem 1. A Social Security Number is a sequence of 9 digits. a. How many Social Security Numbers are possible? b. How many of them begin with either 023 or 003? c. How many Social Security Numbers are possible if no two adjacent digits are the same? (For example, 235-93-2345 is permitted, but not 126-67-8189.) Solution: (a) Steps 1–9 Choose 9 digits: 109 choices for Social Security numbers (b) Alternative 1: Start with 023 Steps 1–8: Choose the remaining 6 digits: 106 choices Alternative 2: Start with 003 Steps 1–3: Choose the remaining 6 digits: 106 choices Total number of choices: 1066+ 106 = 2,000,000 (c) Use the following decision algorithm: Step 1: Select the 1st digit: 10 choices Step 2: Select a 2nd digit different from the 1st digit: 9 choices Step 2: Select a 3rd digit different from the 2nd digit: 9 choices ... Step 9: Select a 9th digit different from the 8th digit: 9 choices Total number of choices: 10 9 8 = 430,467,210