A basketball coach will select the members of a five-player team from among 12 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter? Choose the most appropriate option:
A) 1/9
B) 1/6
C) 2/9
D) 5/33
E) 1/3
you can but that will require more cases and will be time consuming.   straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 10c3   total number of ways of selecting 5 players out of 12 = 12c5   probability = 10c3/12c5 = 5/33   5/33
<result>D</result>
A basketball coach will select the members of a five-player team from among 12 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter?