4. (1994 Hebei Province High School Mathematics Competition) Let the set $A=\{1,2, \cdots, 366\}$. If a two-element subset $B=\{a, b\}$ of $A$ satisfies $17 \mid (a+b)$, then $B$ is said to have property $P$.
(1) Find the number of two-element subsets of $A$ that have property $P$;
(2) Find the number of a set of two-element subsets of $A$, which are pairwise disjoint and have property $P$.
4. (1) Divide $1,2, \cdots, 366$ into 17 classes based on the remainder when divided by 17: $[0],[1], \cdots,[16]$. Number of elements.
(i) When $a, b \in[0]$, the number of subsets with property $P$ is $C_{21}^{2}=210$;
(ii) When $a \in[k], b \in[17-k], k=1,2, \cdots, 7$, the number of subsets with property $P$ is $C_{22}^{1} \cdot C_{21}^{1}=462$;
(iii) When $a \in[8], b \in[9]$, the number of subsets with property $P$ is $C_{22}^{1} \cdot C_{22}^{1}=484$.
Therefore, the number of subsets of $A$ with property $P$ is $210+462 \times 7+484=3928$.
(2) To ensure that the binary subsets do not intersect, when $a, b \in[0]$, 10 subsets can be paired;
When $a \in[8], b \in[9]$, 22 subsets can be paired.
Thus, the number of pairwise non-intersecting subsets with property $P$ is $10+21 \times 7+22=179$.