To find the different line-ups the team can make.

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There are $9$ different positions in baseball team, and the team has $16$ players. To find the different line-ups the team can make.

My solution is $$16P9 = \frac{16!}{(16-9)!}$$

Is the solution correct?

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It depends on whether the order of the lineup matters, but in baseball it usually does (batting order, field positions). In which case, yeah, you're right!