2. Find the sum of all four-digit numbers that can be formed using the digits 1, 2, 3, and 4, where the digits do not repeat.
Solution. In forming the four-digit numbers, we observe that it is a case of permutations without repetition, and their total number is $4!=24$. In the first, second, third, and fourth positions of the four-digit numbers, the digit 1 appears $3!=6$ times. The same applies to the digits 2, 3, and 4. Given this, for the sum $S$ we have:

$$
S=6 \cdot 1000(1+2+3+4)+6 \cdot 100(1+2+3+4)+6 \cdot 10(1+2+3+4)=66660 \text {. }
$$