Consider a cube defined on the following dimension hierarchies:

{day < month < quarter < year}

{supplier < supplier_city < supplier_state}

{product < product_group}.

a. (1pt) Knowing that cuboids are generated by selecting any subset of attributes from the dimension hierarchies such that at most one attribute is selected from each dimension hierarchy find the number of cuboids that can be generated for this cube. Write the formula and make the calculations.

b. (1pt) How many cuboids include the month attribute.

c. (1.5pt) List all the cuboids that include the month attribute.

d. (0.5pt) Is: (year, supplier, month, product_group) a valid cuboid in this cube?