Our first question was how many microstates
give rise to the Win macrostate.
Well, this one was pretty easy because we can
just enumerate all the possibilities.
We have apple-apple-apple,
orange-orange-orange, and so on.
So the correct answer is 5.
Question 2 was a little more tricky.
That question asks how many microstates
give rise to the Lose macrostate,
that is, not all three windows
showing the same fruit.
Well, the easiest way to answer that is
to first figure out
how many total possible microstates
there are for this whole system.
And then subtract out the ones
that we know are Win microstates.
And then we're left with the
Lose microstates.
So our first question is,
"How many possible microstates are there total?"
To calculate that we notice that
for the first window there are total of
five possible fruits that it could be,
and for each one of those there are five
possible fruits that the second window could be,
and for each one of those there are five
possible fruits that the third window could be.
So we get the total number is
5 times 5 times 5, which is 125.
OK, the answer to this one is 125,
but we're not done yet.
That was the total number of microstates.
The number of Lose microstates is the total
number minus the number of Win microstates.
So if you remember that the
Win microstates, there are five of them.
So the total number of
Lose microstates is 120.
That is 125 minus 5.