You are the coach of a high school math team and must choose which team members will represent your school at the state

Question

You are the coach of a high school math team and must choose which team members will represent your school at the state tournament The state has imposed the following requirements i your team can consist of at most 8 members ii at most 6 of these members can be juniors or seniors and iii at most 6 members can be men and iv at most 6 members can be women You have tallied total scores for each team member from the regular season and decide to use the top down algorithm from class processing members in decreasing order of their score after all you want to win Which of the following are guaranteed to be true regardless of the seniority gender and scores of your team Check all that apply Your chosen team is guaranteed to respect all of the state s requirements Your chosen team priority dominates any other team that complies with the state requirements Your chosen team will have 8 members so long as it is possible to find a team with 8 members that meets the state requirements The categories identified by the state form a hierarchy

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