6.2a Sequences

Sequences

A sequence is an ordered list of elements chosen from a set, where elements may be repeated. Directly per the multiplication rule, the total count of sequences of length-$k$, where each element is taken from a set of $n$ elements, can be expressed as
$N=n^k.$

Intuition

The multiplication rule directly shows what sequences are.

Examples

Phone Numbers

The US has a standardized phone number system. Each phone number consists of a country code (always “+1”), an area code (any 3 digits), a telephone prefix (any 3 digits), and a line number (any 4 digits).

How many US phone numbers are there? $N=1\cdot 10\cdot 10\cdot 10\cdot \dots =10^{10}.$

Since the country code is always +1, and all other digits can be any digit from 0-9, then