Final answer:
The number of different samples obtained by selecting three households randomly with replacement from a population of 3 unique households is 27, as each selection is independent and offers 3 choices.
Step-by-step explanation:
To determine how many different samples can be obtained by selecting three households randomly with replacement from a population consisting of unique households numbered 2, 7, and 9, we can use the rule of product for counting outcomes in combination problems.
When sampling with replacement, each selection is independent and has the same number of choices each time. Since there are 3 households and the selection is being made 3 times, each choice has 3 options. Thus, the total number of different samples that can be made is:
3 (choices for first household) x 3 (choices for second household) x 3 (choices for third household) = 3^3 = 27
The correct answer to the question is C) 27.