10. In a 6-cylinder automobile engine, the even numbered cylinders are on the engine’s left side and the odd numbered cylinders are on the right side. (Drawing a picture will help you to visualize this.) A good firing order is a permutation of the numbers 1 to 6 in which the right and left sides are alternated.

(a) How many possible good firing orders are there? (b) Repeat this problem for an engine with 2n cylinders.

Any thoughts? Thanks.