Transcript A Phone Number Dilemma The Counting Principle

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
ABC
NNNN
• 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. 555-01NN