B is reading a book,

C is writing a letter,

Ding is getting a manicure.

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According to the description, A, B and C don't go to manicure, so they can only go to manicure.

And neither A nor C is studying, so only B is studying;

And if A is not lying in bed, then Ding is not getting a manicure, and Ding is getting a manicure, then A is lying in bed;

Obviously, C is writing a letter.