Help with mathematics?

Posted on 2014-12-16 06:05:00 in Math by LEE

A basketball team consists of ?ve players— one centre, two forwards, and two guards. The senior squad at Vennville Central High School has two centres, six forwards, and four guards.

a) How many ways can the coach pick the two starting guards for a game?

b) How many different starting lineups are possible if all team members play their speci?ed positions?

c) How many of these starting lineups include Dana, the team’s 185-cm centre?

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?

e) As the league ?nal approaches, the centre Dana, forward Ashlee, and guard Hollie are all down with a nasty ?u. Fortunately, the ?ve 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.

f) Is the same result achieved if the forwards play their regular positions but the guards can play as either forwards or guards?

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