Question

A developer of a new subdivision wants to build homes that are all different. there are three different interior plans that can be combined with any of five different home exteriors. how many different homes can be built?

Answer 1

Let $I_1, I_2, I_3$ to be interior plans and $E_1, E_2, E_3, E_4, E_5$ to be interior plans.

For each interior plan a develepor has 5 choices of exterior plan that is together 15 possibilities.
(see the attached file for possibility tree)
Answer: 15 different houses.