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

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.