Why isn’t definite article "the" used in “came ___ third in the race”?

Question

There are two sentences. Both of these are correct but why?

1. Neil Armstrong was the first person to walk on the moon.
2. Nick came third in the race.

Why don’t we use "the" in the second sentence?

Answer 1

In the first example, "first" is being used as a determiner; in the second example it is an adverb.

Neil Armstrong was the first person to walk on the moon.

As a determiner, 'first' makes Neil unique in this respect, which is why the definite article is required. Without the determiner, Neil armstrong was just 'a person' that walked on the moon.

You could just as easily re-write this using the adverb:

Neil Armstrong was first to walk on the moon.

Likewise, you could write your second example as:

Nick was the third person to finish the race.