Question

How many 5-digit numbers can be formed using (0-9)?

Answer 1

100 000 combinations

Explanation:

You can have up to 10 combinations for each digit, times the number of... Numbers you want.

So you have `n=10^5=100 000`

Answer 2

`90000`

Explanation:

The trick is to realize that a number can not start with a zero!

Now, there are `10^5` ways in which the digits 0-9 can be chosen for the five places of a five digit number. Out of these, `10^4` start with zero (once we start with 0, there are only 4 slots to fill, where we have 10 choices each).

So, the number of possible five digit numbers is

`10^5-10^4 = 9 times 10^4 = 90000`

These are the numbers 10000 to 99999. We could, of course, just have counted them to get `99999-10000+1 = 90000`