Parshuraam

It was interesting to learn that Parshuraam was the guru of Bhishmapitaamaha, Guru Dronacharya, and Karna.

Karna went to Parshuraam to teach him the valuable knowledge he had. When asked whether he was a Kshatriya, Karna denied since he wasn't aware of the fact that he is indeed a Kshatriya. Eventually the incident with the bumble-bee revealed that Karna was a Kshatriya and not a brahmin. When Parshuraam was resting with his head in Karna's lap, Shri Krishna comes as a bumble-bee to bite Karna and reveal his secrets. The Guru refuses to teach Karna further.

So had Parshuraam had decided only to teach Brahmins or was it to non-Kshatriyas only, was Bhishmapitaamaha a brahmin?