How many possible states could I have in this case?

Hi,
I am really confused and I am not sure whether I should consider this as permutations or combinations problem?

say I have five houses
for each house, I will send and agent how will test the condition of the house and he can record one of three states for the house condition, so the house's condition can be: {good, bad, unchecked}
so these are my questions:
- how many possibilities can I have for the five houses ?
- if I have 2 agents instead of one, how many possibilities can their test result in ?
- is there a formula that I can use to check this when I have more agents ?

I'll really appreciate any help

analeen said:

say I have five houses
for each house, I will send and agent how will test the condition of the house and he can record one of three states for the house condition, so the house's condition can be: {good, bad, unchecked}
so these are my questions:
- how many possibilities can I have for the five houses ?
- if I have 2 agents instead of one, how many possibilities can their test result in ?
- is there a formula that I can use to check this when I have more agents ?

Click to expand...

I suspect that you have gotten no replies because there are several ways to read this question.

The case of one agent is is easy if we assume that he/she rates all five houses: \(\displaystyle 3^5\).

But having more that one agent it depends on what exactly you mean by "possibilities can their test result in".

For two agents and if each rates all five houses and you mean possibilities can their test result in: \(\displaystyle 3^{10}\).
That is the total possible different reports you could receive on the collection of houses.

There are other ways to read this question. Have I come close to what you mean?