Question

From the digits 1, 2, 3, 4, 5, 7, 9, how many numbers of three digits can be formed if repetition is allowed in a number?

Answer 1

Hint: We first find the options we have from the digits 1, 2, 3, 4, 5, 7, 9 to form the 3-digit numbers. We have to fill-up the spots and we find the conditions for the spots as repetition is allowed. We don’t need to worry about 0 for the first spot in the number. For the rest we don’t have restrictions.

Complete step-by-step solution:
We have to find the number of 3-digit numbers that are created from the digits 1, 2, 3, 4, 5, 7, 9.
To create a 3-digit number we have to fill up 3 spots with the given numbers 0 to 9 where repetition is allowed. The main condition is to fill up the spots.
For the first spot we have 7 options as we can use any of the seven digits. For all the other spots of the 3-digit number we have also 7 options as we can do repetition.
So, the total number of choices will be the multiplication of these choices.
The final number will be ${{7}^{3}}$. Therefore, there are ${{7}^{3}}$ 3-digit numbers in total.

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 objective for choosing, for the problem.