12 points I Previous Answers DevoreStat9 2.E.042 A starting lineup in basketball
ID: 3303219 • Letter: 1
Question
12 points I Previous Answers DevoreStat9 2.E.042 A starting lineup in basketball consists of two guards, two forwards, and a center My Notes Ask Your Teache (a) A certain colleg e team has on its roster three centers, four guards, four forwards, and one individual (X) who can play either guard or orward. How many different starting Ineups can be created? (Hint: Consider ineups without X, then lineups with X as guard, then lineups with as forward.] Eineups (b) Now suppose the roster has S guards, 4 forwards, 4 centers, and 2 swing players x and V) who can play either guard or forward. If s of the 15 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.) 1.394 ]Explanation / Answer
(B)
There are total 17 players. 5 Players can be selected in 17C5 ways
If we consider the swing player with their abilities we will have different possible combinations for selections
1. 5 Guards, 6 Forwards, 4 Centers
From this required team can be selected in 5C2*6C2*4C1 = 600
2. 6 Guards, 5 Forwards, 4 Centers
From this required team can be selected in 6C2*5C2*4C1 = 600
3. 7 Guards, 4 Forwards, 4 Centers
From this required team can be selected in 7C2*4C2*4C1 = 504
hence total possible ways of selection are 600+600+504 = 1704
Required probability = 1704 / 17C5 = 0.2754
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