Question

How many 5-digit numbers are there in all?

Answer 1

Hint:
Here to solve this problem we will first need the value of the largest 5- digit number and smallest 5-digit number. Then we will take the difference of the value of largest 5-digit number and the value of smallest 5-digit number. We will then add 1 to the obtained difference. The resulting answer will give the total number of 5-digit numbers.

Complete step by step solution:
We have to calculate the total number of 5-digit numbers.
Let’s take the value of the smallest 5-digit number first which is 10000.
Also, we know that the largest 5-digit number is 99999.
To calculate the total number of 5-digit numbers we need the difference of the value of largest 5-digit number and the value of smallest 5-digit number.
Difference \[ = 99999 - 10000 = 89999\]
So the difference of the value of largest 5-digit number and the value of smallest 5-digit number is 89999.
We will add one to the obtained difference to get the total number of 5-digit numbers.
\[89999 + 1 = 90000\]

So, there are total \[90000\] 5-digit numbers.

Note:
There is an alternate method to solve this problem which is by using Permutations and combinations.
We have to calculate total 5-digit numbers.
In the first place, we can use only 9 numbers and not zero because if we use zero then the resulting number will be a 4 digit number.
In the second, third, fourth, and fifth place, we can allot each place with 10 numbers (from 0-9).
So total number of ways to arrange the numbers would be \[9 \times 10 \times 10 \times 10 \times 10 = 90000\]
Hence, the total number of 5-digit numbers would be 90000.