19. Different positive 3-digit integers are formed from the five digits $1,2,3,5,7$, and repetitions of the digits are allowed. As an example, such positive 3-digit integers include 352, 577, 111, etc. Find the sum of all the distinct positive 3-digit integers formed in this way.
19. Ans: 49950
Number of three-digit integers formed $=5^{3}=125$. Observe that each of the five digits $1,2,3,5,7$ appears 25 times in the first, second and third digits of the integers formed. Thus,
$$
\begin{aligned}
\text { sum }= & 25 \times(1+2+3+5+7) \times 100 \\
& +25 \times(1+2+3+5+7) \times 10 \\
& +25 \times(1+2+3+5+7) \\
= & 49950 .
\end{aligned}
$$