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Chapter 6: Problem 11

A Social Security number has nine digits. How many Social Security numbers are possible?

Short Answer

Expert verified
There are \( 10^9 = 1,000,000,000 \) possible Social Security numbers.

Step by step solution

01

Identify the total digits in a Social Security number

Each Social Security number is a nine-digit number. We have to calculate the number of possible arrangements using these nine digits (0-9).
02

Determine the possible values for each digit

A digit can have a value from 0 to 9, so there are 10 possible values for each digit in a Social Security number.
03

Calculate the number of possible permutations

Since there are 10 possible values for each digit and there are 9 digits in total, we can use the multiplication principle to find the total number of possible Social Security numbers. The multiplication principle states that if there are a ways to do something and b ways to do another thing, then there are a 脳 b ways of doing both. In this case, there are 10 ways to choose the first digit, 10 ways to choose the second digit, and so on, until the ninth digit. The total number of possible Social Security numbers can be represented as: \( 10^1 脳 10^1 脳 10^1 脳 10^1 脳 10^1 脳 10^1 脳 10^1 脳 10^1 脳10^1 \) Or more simply: \( 10^9 \)
04

Calculate the result

Now we compute the result: \( 10^9 = 1,000,000,000 \) So there are 1,000,000,000 possible Social Security numbers.

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Most popular questions from this chapter

In a survey of 200 employees of a company regarding their \(401(\mathrm{k})\) investments, the following data were obtained: 14 I had investments in stock funds. 91 had investments in bond funds. 60 had investments in money market funds. 47 had investments in stock funds and bond funds. 36 had investments in stock funds and money market funds. 36 had investments in bond funds and money market funds. 5 had investments only in some other vehicle. a. How many of the employees surveyed had investments in all three types of funds? b. How many of the employees had investments in stock funds only?

Find the smallest possible set (i.e.. the set with the least number of elements) that contains the given sets as subsets. $$ \\{1,2,4\\},\\{a, b\\} $$

Let \(A, B\), and \(C\) be subsets of a universal set \(U\) and suppose \(n(U)=100, n(A)=28, n(B)=30\), \(n(C)=34, n(A \cap B)=8, n(A \cap C)=10, n(B \cap C)=15\) and \(n(A \cap B \cap C)=5\). Compute: a. \(n[A \cap(B \cup C)]\) b. \(n\left[A \cap(B \cup C)^{q}\right.\)

Let \(A=[2,4,6,8]\) and \(B=\\{6,7,8,9,10\\}\), Compute: a. \(n(A)\) b. \(n(B)\) c. \(n(A \cup B)\) d. \(n(A \cap B)\)

Let \(A=\\{1,2,3,4,5\\}\). Determine whether the statements are true or false. a. \(0 \in A\) b. \(\\{1,3,5\\} \in A\)
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