5. In a certain singles table tennis tournament, it was originally planned that each pair of players would play exactly one match, but after 3 players each played 2 matches, they withdrew from the tournament. As a result, only 50 matches were played in total. The number of matches played among these 3 players is
(A) 0
(B) 1
(C) 2
(D) 3
Answer ( )
(B)
5.【Analysis and Solution】Let the number of matches between the three players be $r$, with a total of $n$ players participating. According to the problem, we have $50=$ $\mathrm{C}_{n-3}^{2}+r+(6-2 r)$, which means $\frac{(n-3)(n-4)}{2}=44+r$. Since $0 \leqslant r \leqslant 3$, it is found that only when $r=1$, $n=13$ is a positive integer.