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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In reply to Re^2: x objects in y containers where all objects are used by Anonymous Monk
in thread x objects in y containers where all objects are used by Ectaris

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