Which of the following statements in the context of tradition of Ajivika relevant in Ancient India is/are correct?

According to the tradition of to the Ajivika, everything is predetermined.

Makkhali Gosala belonged to the Ajivika tradition, characterized by their belief in fatalism, the notion that everything in life is predetermined. King Ajatasattu met him and described the conversation he had with Gosala to Buddha.
Ajita Kesakambalin belonged to the Lokayata tradition, often described as materialist.
Unfortunately, we have limited information about these traditions as their original texts did not survive, and our knowledge of them is derived solely from the writings of other traditions.