Here is the question:
(a) In a six-cylinder engine, the even-numbered cylinders are on the left and the odd-numbered cylinders are on the right. A good ﬁring order is a permutation of the numbers 1 to 6 in which right and left sides are alternated. How many possible good ﬁring orders are there which start with a left cylinder?
b) Repeat for a 2n-cylinder engine.
For for first part, I figured it out with enumeration. I did notice a pattern though: that you have 3 choices then 3 choices , 2 then 2, etc.
For the second part I'm a bit confused about how to do it. I appreciate any tips or advice.