Why the word "Count Rushmore" came up all of a sudden?

Native speaker’s answer
Rebecca
While watching Jeopardy, Joey guesses the answer to be "Count Rushmore." Chandler gets upset later during his conversation with Joey when he finds out that he doesn't like Janice. Thus, he leaves the room and says out of spite, "there is no Count Rushmore!" He is making fun of Joey because the correct answer is Mount Rushmore, the national monument found in South Dakota. Count Rushmore truly doesn't exist.