A starting lineup in basketball consists of two guards, two forwards, and a cent

Question

A starting lineup in basketball consists of two guards, two forwards, and a center. a A certain college team has on its roster five guards, four forwards, and three centers. How many different starting lineups can be created? b Suppose a team has on its roster four guards, four forwards, three centers, and one individual who can play either guard or forward. How many different starting lineups can the team create? (Hint: Consider lineups without the flexible player, lineups with the player as a guard, and lineups with the player as a forward.)

Explanation / Answer

A) Number of possible teams from five guards, four forwards and three centres = 5C2 x 4C2 x 3C1 = 180

B) Number of teams possible when the last individual plays as guard = 5C2x4C2x3C1 = 180

number of teams possible when the last individual plays as a forward = 4C2 x 5C2 x 3C1 = 180

So, number of ways in which lineups can be formed = 180 + 180 = 360

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