A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 32 batteries of each type. (a) How many ways can a total inventory of 32 batteries be distributed among the eight different types? vertical bars and crosses, with the types Following the model of Example 9.6.2, represent each way of distributing the inventory as a string of batteries corresponding to the spaces around the vertical bars and the batteries corresponding to the crosses. It follows that the number of ways the total inventory can be distributed is (b) How many ways can a total inventory of 32 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries? (c) How many ways can a total inventory of 32 batteries be distributed among the eight different types if the inventory includes at most three A76 batteries?