Question

How many 8-digit numbers are there in all?

Answer 1

Hint: We first find the options we have as digit to form the 8-digit numbers. We have to fill-up the spots and we find the conditions for the spots. We can’t use the digit 0 for the first spot in the number. For the rest we don’t have restrictions.

Complete step-by-step answer:
We have to find the number of 8-digit numbers there.
To create an 8-digit number we have to fill up 8 spots with numbers 0 to 9. Repetition is allowed.
The first digit of the 8-digit number can’t be 0 as that will make the number a 7-digit number.
The main condition is to fill up the spots.
For the first spot we have 9 options as we can’t use the digit 0. For all the other seven spots of the 8-digit number we have 10 options as we can use zeroes there.
So, the total number of choices will be the multiplication of these choices.
The final number will be $9\times {{10}^{7}}$.
Therefore, there are $9\times {{10}^{7}}$ 8-digit numbers in total.
So, the correct answer is “ $9\times {{10}^{7}}$”.

Note: We need to be careful about the filling up spots with digits concept as it seems equal to the concept of number of spots for each digit. They are not equal. We always need to keep in mind the actual choosing for the problem.