Question

construct arguments barbara is in charge of the award medals for a sporting event. she has 31 medals to present to various individuals or competing teams. she asserts that at least one team will end up with more than 5 medals. do you believe her assertion? justify your argument.
select choice
select choice 5 medals, then the total number of medals
select choice be more than 5 × 6 or
select choice medals

Explanation:

Step1: Analyze the problem

We have 6 teams and 31 medals. We need to check if at least one team gets more than 5 medals.

Step2: Use the pigeonhole principle

The pigeonhole principle states that if we have \(n\) pigeonholes and \(m\) pigeons with \(m>n\times k\), then at least one pigeonhole has more than \(k\) pigeons. Here, teams are pigeonholes (\(n = 6\)), medals are pigeons (\(m=31\)), and \(k = 5\).
Calculate \(n\times k=6\times5 = 30\).
Since \(31>30\) (i.e., \(m>n\times k\)), by the pigeonhole principle, at least one team will have more than 5 medals.

Answer:

Yes, Barbara's assertion is correct. Using the pigeonhole principle, with 6 teams (pigeonholes) and 31 medals (pigeons), since \(6\times5 = 30<31\), at least one team must have more than 5 medals.