|
||||||||||||
|
||||||||||||
| ||||||||||||
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 one-digit passwords you already have can be extended to a two-digit 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 one-digit password can be extended to $10$ two-digit passwords and hence there are $10 \times 10 = 10^2$ two-digit passwords. Ok, what about
This time each of the two-digit password you already have can be extended to a three-digit password by adding a third digit. Again, in each case there are $10$ choices for the third digit so the number of three-digit passwords is $10$ times what you already had, that is $10^2 \times 10 = 10^3 .$ Repeat this process for four, five and six-digit passwords. I hope this helps, | ||||||||||||
|
||||||||||||
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. |