1. Let $a, b, c$ be positive integers, satisfying $a \leqslant b \leqslant c$, and $a +$ $b+c=15$. Then, the number of triangles with side lengths $a, b, c$ is ( ) .
(A) 5
(B) 7
(C) 10
(D) 15
(Tip: Discuss in 5 categories according to $1 \leqslant a \leqslant 5$. Answer: (B).)