Question B A starting lineup in basketball consists of two guards, two forwards,

Question

Question B

A starting lineup in basketball consists of two guards, two forwards, and a center (a) A certain college team has on its roster three centers, five guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.] 225 lineups (b) Now suppose the roster has 3 guards, 5 forwards, 3 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 13 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.) 470X

Explanation / Answer

b) There are quite a number of legit cases !

2 swings used as guards (g): 2c2 *5c2 *3c1 = 30
2 swings used as forwards (f) : 3c2 *2c2 *3c1 = 9
2 swings used 1g, 1f : 2c1*3c1 *1c1*5c1 *3c1 = 90
1 swing used as g : 2c1*3c1 *5c2 *3c1 = 180
1 swing used as f: 3c2 *2c1*5c1 *3c1 = 90
0 swing used: 3c2 *5c2 *3c1 = 90

legitimate ways = 489
total ways = 13c5 = 1287
Pr = 489/1287 = 163/429 = 0.380 or 0.3799

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