Question

In a different plan for area codes,the first digit could be any number from 3 through 7, the second digit was either 6,7,or8, and the third digit could be any number except 6 or 7. With this plan, how many different area codes are possible?

Answer 1

Explanation:

According to the given plan for area codes, the first digit can be any number from 3 through 7, the second digit can be 6, 7, or 8, and the third digit can be any number except 6 or 7.

There are 5 possible choices for the first digit (3, 4, 5, 6, or 7), 3 possible choices for the second digit (6, 7, or 8), and 8 possible choices for the third digit (0, 1, 2, 4, 5, 8, 9). This is because there are 10 possible digits in total, but we cannot use 6 or 7 for the third digit.

Using the multiplication principle of counting, we can multiply these choices together to find the total number of possible area codes:

5 x 3 x 8 = 120

Therefore, there are 120 different area codes possible with this plan.