Question

How many area codes (abc) would be possible if all three digits could be any vaiue 1-9

Answer 1

There would be 729 possible area codes if each digit can range from 1 to 9 since we multiply the 9 possibilities for each of the three digits to find the total number of permutations.

Step-by-step explanation:

The question is asking how many different area codes can be created if each digit in the area code (abc) can be any number from 1 to 9. This is a question of permutations where repetition is allowed, thus each position in the area code can be any of the 9 possible digits.

For the first digit (a), there are 9 possibilities (1-9). For the second digit (b), there are also 9 possibilities (1-9). Finally, for the third digit (c), there are similarly 9 possibilities (1-9).

To calculate the total number of possible area codes, you would multiply the number of possibilities for each digit: 9 (for a) × 9 (for b) × 9 (for c), which equals 729 possible area codes.

Answer 2

The total number of area codes that would be possible if all three digits could be any value from 1 to 9 is 729.

Step-by-step explanation:

1. Let's start our reasoning to get this answer:

From 000 to 999, we have 1,000 possible area codes.

But for this question, we should find out the answer without considering the digit 0, therefore we must exclude:

A. From 000 to 099, that are 100 possible area codes.

B. We also have to exclude, from 100 to 110, 120, 130, 140, 150, 160, 170, 180 and 190. Those are 19 area codes more.

C. We also have to exclude these same options of code areas, for 200 - 210 and 2x0, and 19 more for each subset that starts with 3, 4, 5, 6, 7, 8 and 9. In total, 19 multiplied by 8, 152 numbers more.

Therefore, the total number of area codes that would be possible if all three digits could be any value from 1 to 9 is:

1,000 - 100 - 19 - 152 = 729

The simplest way to find it, is:

For 000 to 999 = 1,000 or 10³

Excluding the digit zero = 729 or 9³