Question

How many different positive integers can be expressed in k digits using radix r numbers?

Answer 1

Let us take an example with radix 10, using 2 digits we can write from 0,1,23....95,96,97,98 and 99 that is total 100= $10^{2}$ numbers

Similarly using 3 digits, we can write from 0 to 999= 1000 = $10^{3}$ numbers.

Generalizing this we can express $r^{k}$ numbers using k-digits in a radix r.