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.