Assignment:
Q1) Three identical light beams are to be installed in the vertices of a hexagonal tower, ie., hexagonal cylinder, with 12 vertices.
a) No other restriction applies?
b) Only the top vertices are to be used?
c) Only one beam goes at the top?
Q2) There are ten identical books, and one each of 10 different books. How many groups of ten books are there?
Q3) A certain number of shampoo containers are placed in groups of 12, and 8 remain. But, placed in boxes that hold 35, only 2 remain. Find all the possible numbers of containers. In particular, what is the smallest possible number?
Provide complete and step by step solution for the question and show calculations and use formulas.