



 
Hi Judy, Think about the simpler question
The answer is clear, there are $10$ such passwords and you can write them all down, $ 0, 1, 2, \cdot \cdot \cdot, 9.$ Now suppose the question is
Each of the onedigit passwords you already have can be extended to a twodigit password by adding a second digit, so for example $0$ extends to $00, 01, 02, \cdot \cdot \cdot, 09$ and $1$ extends to $10, 11, 12, \cdot \cdot \cdot, 19.$ Thus each onedigit password can be extended to $10$ twodigit passwords and hence there are $10 \times 10 = 10^2$ twodigit passwords. Ok, what about
This time each of the twodigit password you already have can be extended to a threedigit password by adding a third digit. Again, in each case there are $10$ choices for the third digit so the number of threedigit passwords is $10$ times what you already had, that is $10^2 \times 10 = 10^3 .$ Repeat this process for four, five and sixdigit passwords. I hope this helps,  


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