MDM4U - Combinations Question!?
a) How many ways can the coach pick the two starting guards for a game?
for this its 4C2 = 6
b) How many different starting lineups are possible if all team members play their specified positions?
for this its 2C1 x 6C2 x 4C2 = 180
c) How many of these starting lineups include Dana, the team’s 185-cm centre?
for this its 1C1 x 6C2 x 4C2 = 90
d) Some coaches designate the forwards as power forward and small forward. If all six forwards are adept in either position, how would this designation affect the number of possible starting lineups?
for this i think its 1C1 x 6C1 x 5C1 x 4C2 = 360 ???? Correct?
e) As the league final approaches, the centre Dana, forward Ashlee, and guard Hollie are all down with a nasty flu. Fortunately, the five healthy forwards can also play the guard position. If the coach can assign these players as either forwards or guards, will the number of possible starting lineups be close to the number in part b)? Support your answer mathematically.
for this i think its 1C1 x 5C2 x 7C2 = 210???? Correct?
f) Is the same result achieved if the forwards play their regular positions but the guards can play as either forwards or guards? Explain your answer.
2C1 x 8C2 x 4C2 = 336 ???? Correct?