Farmer John's hobby of conducting high-energy physics experiments on weekends has backfired, causing N wormholes (2 <= N <= 12, N even) to materialize on his farm, each located at a distinct point on the 2D map of his farm (the x,y coordinates are both integers).
According to his calculations, Farmer John knows that his wormholes will form N/2 connected pairs. For example, if wormholes A and B are connected as a pair, then any object entering wormhole A will exit wormhole B moving in the same direction, and any object entering wormhole B will similarly exit from wormhole A moving in the same direction. This can have rather unpleasant consequences.
For example, suppose there are two paired wormholes A at (1,1) and B at (3,1), and that Bessie the cow starts from position (2,1) moving in the +x direction. Bessie will enter wormhole B [at (3,1)], exit from A [at (1,1)], then enter B again, and so on, getting trapped in an infinite cycle!
*So no: of possible pairs would be this C(n,2)*C(n-2,2)*C(n-4,2)*C(n-6,2)C(n-8,2).......*
Sorry being so trivial,but i think there might be some kind of formula for this series C(n,2)*C(n-2,2)*C(n-4,2)*C(n-6,2)C(n-8,2)....... like we have for C(n,2)+C(n-2,2)+C(n-4,2)+C(n-6,2)....=2^n-1
But i'am unable to arrive it, if possible even suggest some kind of source for formulae for series of binomial coefficients
So what does this expression amount to