Question

houses in an estate are all identical. however, a person can purchase a new house with some, all, or none of a set of options, as indicated by the set below. how many options are there for purchasing a house in this community? {lake view, upgraded landscaping, pool} there are □ options for purchasing a house in the community.

Explanation:

Step1: Identify number of options

There are 3 distinct optional features: lake view, upgraded landscaping, pool.

Step2: Calculate total combinations

For each feature, there are 2 choices: include it or not. For $n$ independent options, total combinations are $2^n$. Here $n=3$, so:
$2^3 = 2 \times 2 \times 2 = 8$
This includes the case of choosing none of the options.

Answer:

8