# Thread: Any methods on solving this

1. ## Any methods on solving this

If each of the 10 digits is chosen at random, how many ways can you choose the following numbers?

A)A two-digit code number repeated digits permitted
B)A Three digit identification card number, for which the first digit cannot be a 0.

If can answer at least one that would be great and thanks.

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Originally Posted by Shadows
If each of the 10 digits is chosen at random, how many ways can you choose the following numbers?

A)A two-digit code number repeated digits permitted
B)A Three digit identification card number, for which the first digit cannot be a 0.

If can answer at least one that would be great and thanks.
A) There are $\displaystyle 10$ ways of choosing the first digit, and $\displaystyle 10$ ways of choosing the second digit. So there are $\displaystyle 10\times10=100$ ways of choosing the two digits, one after the other. (The codes are, of course, from $\displaystyle 00$ to $\displaystyle 99$ inclusive.)

B) There are only $\displaystyle 9$ choices for the first digit, followed by $\displaystyle 10$ for each of the other two digits. So there are $\displaystyle 9\times10\times10=900$ possible choices altogether.