selango wrote:John and Peter are among the nine players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter?
A. 1/8
B. 1/6
C. 2/9
D. 5/18
E. 1/3

OA D

total no of ways in which 5 player cna be choosen 9c5=9*8*7*6/24=126
now we shld alway sinclude joh and peter so remaining 3 player should be choosen from 7 players which can be done in 7c3=7*6*5/6=35
so 35/126=5/18

The word team should make you think combination.

The question is asking for the following fraction:

(total number of good teams)/(total number of possible teams)

Let's determine each part of this fraction separately.

To determine the total number of possible teams, we need to determine how many combinations of 5 can be made from 9 choices:

(9*8*7*6*5)/(1*2*3*4*5) = 126 total possible teams

A good team will consist of John and Peter put together with 3 other players. Since we know that John and Peter have to be included in a good team, our only concern is the number of ways we can choose the 3 other players from the 7 we have left.

So we need to determine how many combinations of 3 can be made from 7 choices:

(7*6*5)/(1*2*3) = 35 good teams.

So (good teams)/(total teams) = 35/126 = 5/18.