# Phone Numbers and Combinations

Discussion | **Summary** | Extension | Practice

# The Basics

**The fundemental counting states that if you have ****x**** options for one choice, and ****y**** options for another, the number of unique combinations of chosing one of each choice is the product of the two counts of options.**

If you have more than two choices, then it's the same idea: multiply all the number of options you have per choice.

North America uses the *North American Numbering Plan* (NANP). Under this plan, we can get about **792 000 000 numbers.**

**Whenever you apply the fundamental counting principle, be careful about how you count how many options you have. Take note of any exceptions or conditions.**

**Use a calculator. ** BE VERY CAREFUL about the numbers you punch in - long numbers often leads to typos.

As much as possible, simplify your work before writing down your calculation. (See the image to the right - which is easier to type in? A bunch of 10s ten times, or as an exponent? Chances are you'll go with the second option.)

## Useful Numbers

The number of whole-number digits between

*[0-9]*is**10.**The number of letters in the English alphabet, case insensitive, is

**26.**The number of letters in the English alphabet, case sensitive, is

**52.**An

*alphanumeric*set of choices (excluding special characters) is either:

**62**if characters are case sensitive; or**36**if the characers are case insensitive

Your options for a given choice will most likely be given to you if a set of options are not one of these four choices.