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(D) In a tournament with $n=5$ teams,the total number of games played is $\binom{5}{2} = 10$. Each game results in $1$ point for the winner and $0$ fo

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There are at most four teams which have at most two points each.

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(D) In a tournament with $n=5$ teams,the total number of games played is $\binom{5}{2} = 10$. Each game results in $1$ point for the winner and $0$ for the loser,so the sum of points is $10$. Let $s_1, s_2, s_3, s_4, s_5$ be the scores of the teams. We know $\sum s_i = 10$. Option $(d)$ states: "There are at most four teams which have at most two points each." Consider the case where all teams have equal points: $s_1=s_2=s_3=s_4=s_5=2$. Here,all $5$ teams have at most $2$ points. Since $5 > 4$,the statement "at most four teams have at most two points" is false for this scenario. Thus,$(d)$ is not necessarily true.

In a tournament with five teams,each team plays against every other team exactly once. Each game is won by one of the playing teams and the winning team scores one point,while the losing team scores zero. Which of the following is $NOT$ necessarily true?

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