Q.1.5 - A First Course in Probability

Question

 For years, telephone area codes in the United States and Canada consisted of a sequence of three digits. The first digit was an integer between 2 and 9, the second digit was either 0 or 1, and the third digit was any integer from 1 to 9. How many area codes were possible? How many area codes starting with a 4 were possible 

Step-by-Step Solution

Answer

The possible area codes are 144

The area codes starting with a 4 were possible are 18

Step 1 .Given information

Based on the question we have to find out possible area codes where the first digit was an integer between 2 and 9, the second digit was either 0 or 1, and the third digit was any integer from 1 to 9, and area codes starting with a 4 were possible. 

Step 2. Finding the area codes

By using the basic counting principle, possible integers between 2 to 9, there are 8 options for the second digit there is 2 option( 0 or 1) and for the third digit from 1 to 9, 9 options are there. Thus Total options for this case is $8\times 2\times 9=144$,

For the second case for first digit integers starting with a 4, there is only  1 option, for a second there are 2 options and for third digit 9 options.  Hence area codes starting with a 4 were possible  is $1\times 2\times 9=18$