# How many 5-digit numbers can be formed using

How many 5-digit numbers can be formed using $\left(0-9\right)$?
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Explanation:
You can have up to 10 combinations for each digit, times the number of... Numbers you want.
So you have $n={10}^{5}=100000$.
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Step 1
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).
Step 2
So, the number of possible five digit numbers is
${10}^{5}-{10}^{4}=9×{10}^{4}=90000$
These are the numbers 10000 to 99999. We could, of course, just have counted them to get $99999-10000+1=90000$.