vertical bars and crosses, with the types of batteries corresponding to the spaces around the vertical bars and the batteries corresponding to the crosses. It follows that the A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 29 batteries of each type. (a) How many ways can a total inventory of 29 batteries be distributed among the eight different types? Following the model of Example 9.6.2, represent each way of distributing the inventory as a string of number of ways the total inventory can be distributed is (b) How many ways can a total inventory of 29 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 29 batteries be distributed among the eight different types if the inventory includes at most three A76 batteries?