APPLICATIONS

17-36 ■ Fundamental Counting Principle These exercises involve the Fundamental Counting Principle

Social Security Numbers Social Security numbers consists of nine digits, with the first digit between 0 and 6 , inclusive. How many Social Security numbers are possible?

To state:

The number of Social Security numbers possible.

Given:

The social security number consists of 9 digits, with the first digit between 0 and 6, inclusive.

Approach:

By Fundamental Principle of Counting, If two events occur in order and if the first event can occur in m ways and the second can occur can occur in n ways (after the first occurred), then the two events can occur in order in m×n ways.

Calculation:

For the first digit there are seven possible choices, because the first digit is in between 0 and 6, inclusive, digits 7, 8, and 9 are not allowed