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?  Choices:  A) 1/9  B) 1/6  C) 2/9  D) 5/18  E) 1/3
Total possible ways of selecting a 5-member team:   a combination problem, not permutation since order does not matter:   9x8x7x6x5/(5x4x3x2x1) = 126.   The ways of selecting a 5-member team including John and Peter:   It is again a combination, not permutation. Since John and Peter are already included, you don't bother about them any more. The possible ways will be the combination of the rest of the 3 players from the rest of 7 player:   7x6x5/(3x2x1) = 35.   so the probability = 35/126 = 5/18.   Answer is 5/18: 5/18.
<result>D</result>
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?