A tennis coach is trying to put together a team of four players for the forthcoming tournament. For this 7 players are available: males A, Band C; and females W, X, Y and Z. All players have equal capability and at least 2 males will be there in the team. For a team of four, all players must be able to play with each other. But, B cannot play with W, C cannot play with Z and W cannot play with Y. If Y is selected and B is rejected, the team will consist of which one of the following groups?
- AA, C, Wand Y
- BA, C, X and YCorrect
- CA, C, Y and Z
- DA, W, Y and Z
Explanation
Here's a step-by-step breakdown:
- Given: Y is selected and B is rejected.
- Constraint: At least 2 males must be in the team. Since B is rejected, the only way to have at least 2 males is to select both A and C. So far, the team members are A, C, Y.
- We need one more player for the team of four. The remaining available females are W, X, Z (Y is already selected).
Now, let's check the conflicts for each potential fourth player with the current team (A, C, Y):
- If W is selected: The team would be A, C, Y, W. Conflict: W cannot play with Y. So, W cannot be selected.
- If Z is selected: The team would be A, C, Y, Z. Conflict: C cannot play with Z. So, Z cannot be selected.
- If X is selected: The team would be A, C, Y, X. There are no conflicts involving X (B cannot play with W, C cannot play with Z, W cannot play with Y). This team is valid.
Therefore, the team must consist of A, C, X, and Y.
Analyzing the options: A) A, C, W and Y: Invalid because W cannot play with Y. B) A, C, X and Y: This matches our derived team and has no conflicts. C) A, C, Y and Z: Invalid because C cannot play with Z. D) A, W, Y and Z: Invalid because it only has one male (A), violating the "at least 2 males" rule, and also W cannot play with Y, and C (who should be there) cannot play with Z.
The final answer is B.

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