In some problems of occupancy theory we are concerned with t

In some problems of occupancy theory we are concerned with the number of ways in which certain indistinguishable objects can be distributed among individuals, urns, boxes, or cells with at least one in each cell. Find an expression for the number of ways in which r indistinguishable objects can be distributed among cells with at leas one in each cell, and rework the numerical part at Exercise 1.9 with each of the three customers getting at least one loaf of bread.

Solution

selecting n objects from r objects=^rC_n

distributing remaining with our wish=(n)^r-n

therefore the expresssion is:(n)^r-n * ^rC_n *( ⁿP_n)