(Cohen [1978])
- 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?
We can separately permute the 3 left cylinders and the 3 right cylinders and multiply the number of permutations for the total of \(3! \cdot 3! = 36\)
- Repeat for a \(2n\)-cylinder engine.
Generalized calculation above: \(n! \cdot n!\)