User blog comment:Belthazar451/How To Get A Ghazt; Or, So How Does This Binomial Probability Thing Work, Anyway?/@comment-10751008-20130808075100/@comment-7326455-20130809070108

Binomial probability is handy.

Also, one other clever thing about the binomial coefficients is that nCkalso happens to be the number of ways to choose k items out of a set of n items, if the order of the items doesn't matter (it's why the symbol is C, for "choice" or "combination", and is also why the Excel command is COMBIN). For example, to get the number of two-element monsters on any one island, you're picking two elements from a set of four available elements, which is 4C2 = 6.

If the order of the objects you pick out does matter (for example, if Air+Water resulted in different monster to Water+Air), there's a different one: nPk = n!/(n-k)! - P for "permutations". It doesn't get used in binomial probability, though. Unlike nCk,  nPk is not symmetrical. 4P2 = 12.