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?
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?