Q27. - Algebra 2

Question

In 1995, the restriction on the middle digit was removed, allowing any digit in that position. How many total codes were possible after this change was made?

Step-by-Step Solution

Answer

The number of possible area codes after the change in 1995 is 800.

Step 1. Given Information.

Given that before 1995, area codes had the format (XYZ)

where X = 2,3, …, or 9

Y = 0 or 1

Z = 0, 1, 2, …, or 9

In 1995, the restriction on the middle digit was removed, allowing any digit in that position. It is to be determined how many area codes were possible after the change was made in 1995.

Step 2. Calculation .

For X there are 8 ways to be selected.

Since the restriction on the middle digit was removed, for Y there are 10 ways to be selected.

 

For Z there are 10 ways to be selected.

By the Fundamental Counting Principle, there are $8\times 10\times 10=800$ different ways to select the 3-digit area code.

Step 3. Conclusion .

Hence, the number of possible area codes after the change in 1995 is 800.