Teng is designing a house and in each room he can choose from tiles, floorboards, or carpet for the floor.

a. How many combinations of flooring materials are possible if her designs a 2 room studio?
b. How many combinations are possible for a 3 room apartment?
c. How many combinations for a 4 room flat?
d. How many combinations for an "n" room house?
e. He finally decides on an 8 room house. How many different combinations are possible?

To find the number of combinations of flooring materials for each scenario, we need to consider that Teng can make an independent choice for each room. Since Teng can choose from three options (tiles, floorboards, or carpet) for each room, we need to multiply the number of options for each room together to calculate the total number of combinations.

a. For a 2 room studio:
The number of combinations is calculated as: 3 options for the first room * 3 options for the second room = 3 * 3 = 9 combinations.

b. For a 3 room apartment:
The number of combinations is calculated as: 3 options for the first room * 3 options for the second room * 3 options for the third room = 3 * 3 * 3 = 27 combinations.

c. For a 4 room flat:
The number of combinations is calculated as: 3 options for the first room * 3 options for the second room * 3 options for the third room * 3 options for the fourth room = 3 * 3 * 3 * 3 = 81 combinations.

d. For an "n" room house:
The number of combinations can be calculated as: 3^n, where n represents the number of rooms in the house. Each room has 3 options, so we multiply 3 by itself n times.

e. For an 8 room house:
The number of combinations is calculated as: 3 options for each room * 3 options for each room * 3 options for each room * 3 options for each room * 3 options for each room * 3 options for each room * 3 options for each room * 3 options for each room = 3^8 = 6561 combinations.