In a 10 floor dormitory, each floor has 10000 rooms and all the rooms have series numbers. Assume that 10 people are arranged to reside in each floor, answer the following questions about the ways for allocating tenants into the rooms.

A) if the names of these 100 people are unknown and the number of people living in a room is unlimited , then are there how many ways to distribute the students?

B) if the names of these 100 people in the building are still unknown but a room is allowed to lodge one tenant at most , then are there how many ways of room occupation?

C) the allocation manners of (b) are included in that of (a) and takes up the major part of(a), prove the statement.