A Phone Number Dilemma The Counting Principle AQR

Counting Principle If there are m ways for Event A to occur and n ways for Event B to occur, then there are m × n ways for Events A and B to occur together. Example: How many different ways can one wear 5 different types of shirts, 6 different color of pants, and 4 different color of socks.

Counting Principle Another Example: You are buying a new car. You have two body styles to choose from: sedan and hatchback You have 5 colors to choose from. You have 3 models to choose from: GL – Standard model SS – Sports model SL – Luxury model with leather seats

Counting Principle Another Example: You are buying a new car. Same as the above, but the restriction is that the hatchback cannot be black.

A phone number has 3 sections XYZ-ABC-NNNN: XYZ ABCNNNN Area Code Exchange Code Station Code Today we can assign numbers according to following rules X can be any digit from 2 to 9 Y can be any digit from 0 to 8 Z can be any digit from 0 to 9 A can be any digit from 2 to 9 B, C, and N can be any digit from 0 to 9

2 other restrictions exist B and C both cannot be 1 at the same time. Such at 611 and other special numbers (Hint these restrictions must be subtracted) There are two forms of special numbers that are only used for television and movies NN