Re^2: x objects in y containers where all objects are used

This could be classical recurrence problem. We need some formula, and then a module to convert that into values or count of possibilities.

T(N,2) = N-1;
T(N,K) = SIGMA(T(N-X,K-1)) for X = 1 to N-K  

Example: T(5,3) = T(4,2)+ T(3,2) + T(2,2)
                = 3 + 2 + 1 = 6
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Re^3: x objects in y containers where all objects are used by ikegami (Patriarch) on Nov 07, 2009 at 23:23 UTC
The OP specifically said he didn't want the count. The count is easy to get without even using recursion. It's a simple Combination: `C($num_objects-1, $num_containers-1) = C(4, 2) = 4! / (4-2)! / 2! = (43) / (21) = 6` [download]	[reply] [d/l]