# Math 1508 Quiz # 5

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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

```
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