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, B and C; and females W, X, Y and Z. All players have equal capability and at least two 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?

Correct Option (B)

: A, C, X and Y

The problem specifies the following conditions and constraints:

• Team size: Four players.
• Available players: Males (A, B, C); Females (W, X, Y, Z).
• Constraint 1: At least two males must be in the team.
• Constraint 2: All players must be able to play with each other.
• Conflict 1: B cannot play with W.
• Conflict 2: C cannot play with Z.
• Conflict 3: W cannot play with Y.
• Given conditions for this specific scenario: Y is selected, and B is rejected.

Step-by-step derivation:

1. Given that Y is selected. According to Conflict 3 ("W cannot play with Y"), if Y is in the team, W must be rejected.
2. Given that B is rejected.
3. The initial pool of players is {A, B, C, W, X, Y, Z}.
4. After applying the given conditions (Y selected, B rejected) and the derived condition (W rejected), the remaining available players for selection are:
   • Males: A, C
   • Females: X, Y, Z (W is out)
5. The team needs four players, and Y is already selected. Thus, three more players must be chosen from {A, C, X, Z}.
6. Applying Constraint 1 ("at least two males will be there in the team"): Since A and C are the only available males, both A and C must be selected to meet this requirement.
7. At this point, the team includes A, C, Y. One more player needs to be selected from the remaining available females: X, Z.
8. Applying Constraint 2 ("all players must be able to play with each other") and Conflict 2 ("C cannot play with Z"): Since C is already in the team, Z cannot be selected.
9. Therefore, X must be the fourth player selected.

The final team composition is A, C, X, Y.

This team satisfies all conditions:

• It has four players (A, C, X, Y).
• It has two males (A, C), meeting the "at least two males" requirement.
• Y is selected and B is rejected, as per the given conditions.
• All compatibility rules are met: B (rejected) cannot play with W (rejected); C (selected) can play with A, X, Y (Z is rejected); W (rejected) cannot play with Y (selected).

Incorrect Options:

• Option A: A, C, W and Y

  This option includes both W and Y. This violates the rule that "W cannot play with Y". Therefore, this option is incorrect.

• Option C: A, C, Y and Z

  This option includes both C and Z. This violates the rule that "C cannot play with Z". Since C must be selected to meet the two-male requirement, Z cannot be part of the team. Therefore, this option is incorrect.

• Option D: A, W, Y and Z

  This option includes both W and Y, which violates the rule "W cannot play with Y". Additionally, it includes only one male (A), which violates the constraint that "at least two males will be there in the team". Therefore, this option is incorrect.