All United States social security numbers (which consist of...

Name: Problem 37, Chapter 12: Discrete Mathematics with Applications
Uploaded: 2021-10-21T02:38:20-08:00
Duration: 3 min 18 s
Channel: Nick Johnson
Description: All United States social security numbers (which consist of three digits, a hyphen, two digits, another hyphen, and finally four more digits), where the final four digits start with a 3 and end with a 6 .

All United States social security numbers (which consist of three digits, a hyphen, two digits, another hyphen, and finally four more digits), where the final four digits start with a 3 and end with a 6 .

Key Concepts

Regular Expressions

Regular expressions are a powerful tool for defining search patterns and matching strings in text. They allow users to specify sequences of characters, including fixed characters, wildcards, and special symbols, to describe complex string formats in a concise and flexible manner.

Character Classes

Character classes are used to define a set of characters that can match at a specific position in a string. For instance, specifying digits or letters in a regular expression helps in matching patterns where only certain types of characters are allowed.

Quantifiers

Quantifiers in regular expressions specify how many times a preceding element should appear in the target string. They are crucial for matching patterns with fixed lengths, such as ensuring that a sequence of digits appears a specific number of times.

Literal Characters and Escaping

Literal characters are those that are interpreted exactly as they appear in a regular expression. When working with symbols that have special meanings, such as hyphens or parentheses, escaping them allows the expression to match the actual character rather than invoking its special function.

Transcript

0:00 Hello.

00:01 So here in part a, we're looking to find how many social security numbers are possible.

00:06 Now, a social security number is a sequence of nine digits.

00:10 So for our decision algorithm, well, for step one, we choose a digit for the first slot.

00:15 So that's 0, 1, 2, 4, 5, 6, 7, 8, or 9.

00:19 So that's going to be 10 choices.

00:22 And likely for step 2 for the second slot, again, 0 to 9, again, 10 choices.

00:26 So we have 10 times 10 times 10, right, times 10, right? so we have one, two, three, four, five, six, seven, eight, nine slots.

00:39 So we have nine times ten times, ten times, ten times ten times ten times nine times.

00:43 So that's ten to the ninth power.

00:47 Or it's going to be a one with nine zeros.

00:52 So what number is that? that's going to be, let's see here, one's ten to hundreds, thousands, 1 ,000, 10 ,000, 100 ,000, 1 million, 10 million, 100 million, 1 billion.

01:01 That's 1 billion, 1 billion social security numbers are possible.

01:08 Now for step part b, we want to find the social security numbers that start with either 023 or 0 .03.

01:19 So to do that, well, for alternative 1, the number starting with 023, we have that the 3 digit are fixed.

01:27 So for the remaining six slots, we can pick 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

01:33 So we have 10 choices.

01:35 So we just have but six slots...

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