School A has Principal - P1, Vice-Principal - VP1 and 3 Male Teachers - M1, M2 and M3. School B has Principal - P2, Vice-Principal - VP2 and 2 Female Teachers - F1and F2. An interschool competition is being held between School A and School B. For this, three judgement teams are to be formed such that [1] to make the judgement fair, at least one person from each school must be in each judgement team, [2] at least one of P1, P2, VP1 and VP2 must be selected in each judgement team. If VP2 and F2 are in one of the teams, which of the following could be in the other team?
Solution
School A: P1, VP1, M1, M2,M3
School B: P2, VP2, F1, F2
Option A: P2, F1, M2
If P2, and F1 are both in the second team, no member of school B would be left to participate in the third team. Hence, this team is not possible.
Option B: M2, F1, M1
This does not satisfy the second condition of each team having at least one of, P1, P2, VP1, VP2
Option C: M2, P2, M3
This option satisfies both the conditions.
Option D: P2, F1, VP1
If P2 and F1 are both in the same team, this option too would not leave any member of school B to participate in the third team. Hence, this team is not possible.
Therefore, Option C is the correct answer.
