Lucy doesn't play a wind instrument, but you didn't specify the instruments she could play. If you meant Lucy chooses from any of the four instruments mentioned, then it would be impossible to determine which one Lucy plays based on that information alone. If Lucy can only choose from the named instruments (i.e., we are certain she has to play one of the 4 mentioned instruments), then I can help determine her instrument from the information that has been given. For the instrument named, it wouldn't make sense for John, Mary, and Pete all to play different instruments, as that would mean no one is playing bass. So if the list of instruments was complete and wind instruments must exclude the flute, then Lucy could only play either drums, bass, or trumpet based on what's known. This assumes her instrument is one of these named ones. Let me know if that assumption is correct.