Question

A house with a square floor plan is to have each of its outer four walls fin- ished with brick, stone, stucco, or wood. If no two adjacent outer walls are to have the same finish, in how many ways can the house’s walls be constructed? (One such way is brick on the front and back and stone on the left and right.)

Answer 1

Answer: The answer is 84 ways

Explanation: A house with a square floor plan is to have each of its outer four walls fin- ished with brick, stone, stucco, or wood. However, If no two adjacent outer walls are to have the same finish, there are 84 ways the house walls will be constructed. One of such way is brick on the front and back and also stone on the left and right.