3. If in the three common logarithms $\lg a \sqrt{ } \lg b \sqrt{\lg c}$, the sum of the mantissas of any two is greater than the mantissa of the third, then the three positive numbers $a, b, c$ are said to form a “logarithmic triangle”. Now, choose three distinct integers from the set
$$
M=\{7,8,9,10,11,12,13,14\}
$$

to form a logarithmic triangle, then the number of different selection schemes is ( ) .
(A) $2 \mathrm{C}_{4}^{2}$
(B) $\mathrm{C}_{3}^{3}+\mathrm{C}_{4}^{3}$
(C) $\mathrm{C}_{7}^{3}$
(D) $\mathrm{C}_{8}^{3}$
3.A.

Obviously, the mantissa of $\lg 10$ is 0, so we only need to consider the ternary groups that can form a triangle from the logarithms of the numbers in $M_{1}=\{7,8,9, 1.1,1.2,1.3,1.4\}$. We divide $M_{1}$ into two subsets:
$$
A=\{7,8,9\} \text { and } B=\{1.1,1.2,1.3,1.4\} \text {. }
$$

Note that, if $1\lg c$, i.e., $a b>c$.
Thus, the three numbers in $A$ can form a logarithmic triangle $(7,8,9)$;
The logarithmic triangles that can be formed from $B$ are
$(1.1,1.2,1.3),(1.1,1.3,1.4),(1.2,1.3,1.4)$;
Taking one number from $A$ and two numbers from $B$ cannot form a logarithmic triangle;
Taking two numbers from $A$ and one number from $B$ to form a logarithmic triangle, the cases are:
$(1.2,7,8),(1.2,8,9),(1.3,7,8),(1.3,7,9)$,
$(1.3,8,9),(1.4,7,8),(1.4,7,9),(1.4,8,9)$.
In total, there are 12 groups, which equals $2 \mathrm{C}_{4}^{2}$.