Passage

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 in the team. For a team of four, all players must be able to play with each other. However: B cannot play with W, C cannot play with Z, and W cannot play with Y.

QUESTION

CSAT

Easy

Maths

Prelims 2013

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

Select an option to attempt

Explanation

Combination Formula: $^nC_r = \frac{n!}{[r!(n-r)!]}$

Step 1: Select all three males. Since all three males are selected, there is only 1 way to choose them.

Step 2: Select the fourth member from the remaining individuals. If there are N individuals in total, the number of remaining candidates is N - 3. The fourth member is chosen from these N - 3 individuals.

Number of ways to select the fourth member = $^{(N-3)}C_1 = (N - 3)$

Example: If there are 5 individuals in total (3 males and 2 females): Remaining candidates = $5 - 3 = 2$ Number of ways to select the fourth member = $^2C_1 = 2$