A tennis coach is trying to put together a team of four players for the forthcoming tournament. For this 7 pla

Question

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

Accepted Answer

Here's a brief explanation:

1.  **Fixed Members:** The question states that all three males (A, B, C) are selected.
2.  **Remaining Slot:** Since the team needs four players, and three males are already selected, one more player must be chosen. This player must be a female from the available W, X, Y, Z.
3.  **Applying Restrictions for the Female Player:**
    *   "B cannot play with W": Since B is in the team, W cannot be selected.
    *   "C cannot play with Z": Since C is in the team, Z cannot be selected.
    *   "W cannot play with Y": This restriction is not relevant here because W has already been ruled out, so Y can be chosen independently.
4.  **Valid Female Choices:**
    *   W is out.
    *   Z is out.
    *   X has no restrictions with A, B, or C, so X is a valid choice.
    *   Y has no restrictions with A, B, or C, so Y is a valid choice.
5.  **Possible Teams:**
    *   Team 1: A, B, C, X
    *   Team 2: A, B, C, Y

Therefore, there are 2 possible combinations of four-member teams.

The final answer is B.

Answer

1

Answer

2

Answer

3

Answer

4

Explanation

Related questions