Question

What is the formula to get 4-digit combinations from numbers 0-9?

Answer 1

Hint: We first find the options we have as digit to form the 4-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 numbers with 4-digit combinations from number 0-9.
The choices for the places of the 4-digit combinations is 10.
For the first number we cannot use 0 as that will convert the 4-digit combinations into a number of 3-digit combinations.
As we are creating numbers and no particular condition is mentioned, we can have repetitions.
Therefore, for the first spot we have 9 options as we can’t use the digit 0. For all the other three spots of the 4-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 numbers will be $9\times {{10}^{3}}=9000$.

Therefore, there are 9000, 8-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 choice for the problem.