4.2. (Belgium, 79). Find the sum of all $7!$ numbers that can be obtained by all possible permutations of the digits in the number 1234567.
4.2. For any values of $i, i \in\{1 ; \ldots ; 7\}$, the number of numbers in which the $i$-th place is occupied by the digit $j$ is 61. Therefore, the sum of all numbers is

$$
\begin{aligned}
& (61 \cdot 1+\ldots+61 \cdot 7)+(61 \cdot 1+\ldots+61 \cdot 7) 10+ \\
& \quad+(61 \cdot 1+\ldots+61 \cdot 7) 10^{2}+\ldots+(61 \cdot 1+\ldots+61 \cdot 7) 10^{6}= \\
& =61(1+2+\ldots+7)\left(1+10+\ldots+10^{6}\right)=720 \cdot 28 \cdot 1111111=22399997760 .
\end{aligned}
$$