Some musical instruments have valves that can be either opened or closed to produce different tones. How many tones can be produced by a horn that has 

\((a)\) two valves,

(b) three valves, and

(c) six valves?

(d) Some trumpet players do something called half-valve work, where they play a valve that is neither fully open nor fully closed. If this technique adds a third possible valve setting, how many tones can be produced with a trumpet that has three valves by a player doing half-valve work?