Permutations with independent states

[IE00]

Hello,

I am aware of the formula for working out permutations without repetitions n!/[(n-r)!r!]. But this relates to the n being a pool of choices. ,,,,,, edited

However my query is for permutations with independent states that can be selected each time.

I have a computer which gives either a yes, no or maybe answer. There are x questions it needs to answer. How many different permutations are possible if the computer just gives either a yes or maybe answer for 3 questions? I have worked this out manually and it is six. How many different permutations for a yes or maybe answer for 4 questions? Is there a formula I can use?

 

[pka]

How many different permutations are possible if the computer just gives either a yes or maybe answer for 3 questions? I have worked this out manually and it is six.

If there are just two options, yes or maybe then the answer is \(\large 2^3=8\) not \(\large 6\)
\(\begin{array}{*{20}{c}}
I&{II}&{III} \\
\hline
y&y&y \\
y&y&m \\
y&m&y \\
y&m&m \\
m&y&y \\
m&y&m \\
m&m&y \\
m&m&m
\end{array}\)
If the above is mistaken the you need to explain again.

 

[IE00]

Hi pka,

Thank you for your reply

Okay so I was correct then which is, is the formula is n^x where n is the different states and x of questions? I'd appreciate a formula please if you have one.