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A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster four centers, four guards, five 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.] lineups (b) Now suppose the roster has 3 guards, 4 forwards, 3 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 12 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)

A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster four centers, four guards, five 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.] lineups (b) Now suppose the roster has 3 guards, 4 forwards, 3 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 12 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.1: Counting
Problem 84E
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A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster four centers, four guards, five 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.] lineups (b) Now suppose the roster has 3 guards, 4 forwards, 3 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 12 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)
Transcribed Image Text:A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster four centers, four guards, five 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.] lineups (b) Now suppose the roster has 3 guards, 4 forwards, 3 centers, and 2 "swing players" (X and Y) who can play either guard or forward. If 5 of the 12 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.)
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