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

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, B and 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 combination of four member teams are possible? 

(a) 1 (b) 2 (c) 3 (d) 4

Answer 1

(b) If males A, B and C are selected, we need to select only one more person to make up a four member team. As B is selected, W cannot be selected and as C is selected, Z cannot be selected. So the choice is between X and Y. Then we have the following possibilities :

(A, B, C, X) and (A, B, C, Y)

So, we have two options of team.