What county is Carmel IN in

Carmel city is located Hamilton County.

180 kilometers from San Francisco, the town of Carmel-by-the Sea, on the Californian coast, boasts of not having lampposts, mailboxes, street numbers, neon lights, junk food outlets… And having counted as mayor the director of ‘Invictus’ or ‘Mystic River’, who still lives here.

What is the County of Carmel in?
What cities make up Hamilton County Indiana?
What does Hamilton County include?

Is Carmel a rich town?