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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 three 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 (b) Now suppose the roster has 3 guards, 4 forwards, 4 centers, and 2 "swing players" (X and Y) who can play either guard or forward. i.e exactly two guards, two guards, two forwards, and one centers are chosen) Hint: use part (a) Please explain the steps you took to solve it so that I can learn the appropriate methods. Any help would be appreciated!

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