How many phone numbers can be made if all the digits (that is, 10 digits) need to be filled in and any single digit number (0-9) can be used for any digit?

I don't think any area codes in The US or Canada start with 0 or 1, but ...

if anything goes ......

number of possible phone numbers = 10^10 or 10 Billion

To find the number of phone numbers that can be made when all the digits need to be filled in and any single digit number (0-9) can be used for any digit, we need to calculate the total number of possible combinations.

Since we have 10 digits (0-9) and 10 digits need to be filled in, we can use the concept of permutations with repetition. In this case, repetition is allowed because the same digit can be used more than once.

The formula to calculate the number of permutations with repetition is:

Number of permutations = (Number of options) ^ (Number of positions)

In this case, the number of options is 10 (as we have 10 digits) and the number of positions is also 10 (as all 10 digits need to be filled in).

Therefore, the number of phone numbers that can be made is:

Number of permutations = 10^10

Calculating this expression:

10^10 = 10,000,000,000

So, there can be 10 billion (10,000,000,000) phone numbers that can be made.

To find the number of possible phone numbers, we need to count the different choices we have for each digit. Since any single digit number (0-9) can be used for any digit, we have 10 choices for each digit.

Since a phone number has 10 digits, we multiply the number of choices for each digit (10) together:

10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10^10

Therefore, there are 10^10 possible phone numbers that can be made.