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 all the three males are selected, then how many combinations of four member teams are possible?

Correct Option (B)

The problem states that all three males (A, B, C) are selected for the four-member team. This implies that one additional player, a female, must be chosen from the available females (W, X, Y, Z).

The following compatibility restrictions must be applied:

• B cannot play with W. Since male B is selected, female W is excluded from the team.
• C cannot play with Z. Since male C is selected, female Z is excluded from the team.

Considering these exclusions, the only eligible females remaining for the fourth position are X and Y. The restriction "W cannot play with Y" becomes irrelevant in this specific scenario, as W has already been excluded, and only one female is being selected.

Therefore, the two possible four-member teams are:

• (A, B, C, X)
• (A, B, C, Y)

This results in a total of 2 possible combinations.

Incorrect Options:

Options 1, 3, and 4 are incorrect because, based on the systematic application of the given conditions and compatibility restrictions, precisely two combinations are possible when all three males are selected. Selecting fewer (Option 1) or more (Options 3 and 4) combinations would contradict the derived result.