57 The number of $n(\geqslant 3)$-digit numbers formed by the digits $1,2,3$, with each digit used at least once, is
A. $3^{n}-3 \cdot 2^{n}-3$
B. $3^{n}-3 \cdot 2^{n}+3$
C. $3^{n}-3 \cdot 2^{n}$
D. $3^{n}-2^{n}-3$
57 B. The number of $n$-digit numbers composed of the digits $1,2,3$ is $3^{n}$. Among them, the $n$-digit numbers that contain at most two different digits are $C_{3}^{2} \cdot 2^{n}$; the $n$-digit numbers that contain only one digit are $C_{3}^{1} \cdot 1^{n}$. Therefore, the number of $n$-digit numbers that satisfy the condition is $3^{n}-C_{3}^{2} \cdot 2^{n}+C_{3}^{1} \cdot 1^{n}=3^{n}-3 \cdot 2^{n}+3$ (numbers).