11. (10 points) Football teams $A, B, C, D, E$ are in a round-robin tournament (each pair of teams plays one match). In each match, the winning team gets 3 points, the losing team gets 0 points, and in case of a draw, both teams get 1 point. If the total points for teams $A, B, C, D$ are $1, 4, 7, 8$, respectively, please answer: What is the maximum number of points that team $E$ can get? What is the minimum number of points that team $E$ can get?
11. (10 points) Football teams $A, B, C, D, E$ are in a round-robin tournament (each pair of teams plays one match). Each match awards 3 points to the winning team and 0 points to the losing team, and in the case of a draw, each team gets 1 point. If the total points for teams $A, B, C, D$ are $1, 4, 7, 8$ respectively, what is the maximum and minimum number of points that team $E$ can get?
【Analysis】5 football teams in a round-robin tournament play a total of $4+3+2+1=10$ matches. According to the scoring rules, a match with a winner and a loser awards 3 points, while a draw awards 2 points in total. The problem asks for the maximum and minimum points that team $E$ can get, which clearly depends on the number of draws in the entire tournament. The fewer the draws, the higher the points for team $E$; the more the draws, the lower the points for team $E$. Assuming all matches award 3 points, the total for 10 matches is 30 points, and each draw reduces the total by 1 point.
From the points of $A, B, C, D$, we can analyze as follows.
【Solution】From the problem, we have:
$$
\begin{array}{c}
A=1=1+0+0+0 \\
B=4=3+1+0+0=1+1+1+1 \\
C=7=3+3+1+0 \\
D=8=3+3+1+1
\end{array}
$$

From the points, there are at least 3 draws. The total points for all matches is $30-3=27$ (points). The maximum points for team $E$ is $27-1-4-7-8=7$ (points).

From the points, there are at most 5 draws. The total points for all matches is $30-5=25$ (points). The minimum points for team $E$ is $25-1-4-7-8=5$ (points).

Answer: Team $E$ can get a maximum of 7 points and a minimum of 5 points.