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.