Average of all 6 digit numbers that contain only digits $1,2,3,4,5$ How do I find the average of all $6$ digit numbers which consist of only digits $1,2,3,4$ and $5$?
Do I have to list all the possible numbers and then divide the sum by the count? There has to be a more efficient way, right?
Thank you!

The digit $1$ will contribute $111,111\cdot 5^5$ to the sum of all such $6$ digit numbers.  Similarly, the digit $2$ will contribute $222,222\cdot 5^5$ to the sum.
Continuing, we obtain the sum:
$$(111,111+222,222+333,333+444,444+555,555)\cdot 5^5=3\cdot(555,555)\cdot5^5$$
Divide this by the total number of such $6$ digit numbers ($5^6$) to obtain an average of $333,333$.
