College Algebra & Trigonometry, 2018a

7.1. THE FUNDAMENTAL PRINCIPLE OF COUNTING 309
Exercises 7.1
1) A multiple choice test has 8 questions with four choices (a, b, c, d) for each
question. How many different ways can the test be completed?
2) Local telephone numbers consist of seven digits. Given that the first number
cannot bea0or1,howmany different phone numbers are possible?
3) Nationally, phone numbers consist of of 10 digits - 3 for the area code and
7 for the local number. Before the 1990’s the digits used in the area code were
restricted so that the first digit couldn’t be a 0 or a 1 and the second digit had to
be a 0 or a 1. This was changed to allow for more phone numbers. A useful way
to describe the original plan and the new plan is as follows:
Let X represent any number0-9
Let N represent any number2-9
Let Y represent any number0-1
In this set-up, under the old plan all phone numbers had to adhere to a format of:
NYX NNX XXXX
The reasons for these restrictions had to do with the switching apparatus used by
the phone company.
Under the new plan, phone numbers must follow the format:
NXX NXX XXXX
How many phone numbers are possible under the old plan?
How many phone numbers are possible under the new plan?
How many phone numbers are possible under the new plan for a state that has
only one area code?