A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 30 batteries of each type. (a) How many ways can a total inventory of 30 batteries be distributed among the eight different types? inventory as a string of vertical bars and Following the model of Example 9.6.2, represent each way of distributing 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 1272048 crosses, with the types of batteries corresponding to x. (b) How many ways can a total inventory of 30 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 30 batteries be distributed among the eight different types if the inventory includes at most three A76 batteries?

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