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?
My approach with combinations:
Total number of outcomes = C(5, 9)
Favourable outcomes = C(2,2)*C(3,7)
C(2,2) – number of ways to select two desired players from two… Really doesn’t needed, since it’s 1; I just put it here for clarity sake.
C(3,7) – number of ways to select three other players (NOT John and Peter) from remaining 7
Overall, P= C(3,7)/ C(5, 9) = 5/18.
This is D.