I'm trying to solve a question involving permutations with conditions.
I was reading the following problem:
Five runners competed in a race: Fred, George, Hermione, Lavender, and Ron.
Fred beat George.
Hermione beat Lavender.
Lavender beat George.
Ron beat George.
Assuming there were no ties, how many possible finishing orders could there have been, given only this information?
From the information given, I figured out that George (G) came last.
So, the finishing order was betwen Fred (F), Hermione (H), Lavender (L) and Ron (R).
Now I know from this list that there are
$$4 \times 3 \times 2 \times 1 = 24$$ ways to arrange the final order. But I can't seem to convert the information
Hermione beat Lavender
to find the final answer. I'm stuck. How do I get to the final answer, which is C?