3. Let $a$, $b$, and $c$ be positive integers, and $a \geqslant b \geqslant c$, satisfying $a+b+c=15$. Then the number of triangles with side lengths $a$, $b$, and $c$ is ( ) .
(A) 5
(B) 7
(C) 10
(D) 12
3. B.

The solution can be found using enumeration:
$$
\begin{array}{l}
(7,7,1),(7,6,2),(7,5,3),(7,4,4), \\
(6,6,3),(6,5,4),(5,5,5),
\end{array}
$$

There are 7 pairs in total.