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

Mar 19, 2018

100 000 combinations

#### Explanation:

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

So you have $n = {10}^{5} = 100 000$

Mar 19, 2018

$90000$

#### 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 $99999 - 10000 + 1 = 90000$