8. If: (1) $a, b, c, d$ all belong to the set $\{1,2,3,4\}$; (2) $a \neq b, b \neq c, c \neq d, d \neq a ;$ (3) $a$ is the smallest among $a, b, c, d$. Then, the number of different four-digit numbers $\overline{a b c d}$ that can be formed is $\qquad$ .
8. 28 When $\overline{a b c d}$ has exactly 2 different digits, a total of $C_{4}^{2}=6$ different numbers can be formed;

When $\overline{a b c d}$ has exactly 3 different digits, a total of $C_{3}^{1} C_{2}^{1} C_{2}^{1}+C_{2}^{1} C_{2}^{1}=12+4=16$ different numbers can be formed; when $\overline{a b c d}$ has exactly 4 different digits, a total of $A_{3}^{3}=6$ different numbers can be formed.

Therefore, a total of $6+16+6=28$ different numbers can be formed.