This is a very primordial doubt... from the gurukul days of the princes.
Commonly, everyone believes that Karna was rejected by Drona and then he went to Parasurama to learn, and this rejection was due to caste reasons.
Why do people think so, when in the Mahabharata, it is clearly stated that Karna learnt from both Dronacharya and Parasurama?
Karna was a student of Dorna, but he went to Parasurama to gain knowledge about divine weapons.
[quote] Then Drona endued with great prowess taught the sons of Pandu (the use of) many weapons both celestial and human. And, O bull of the Bharata race, many other princes also flocked to that best of Brahmanas for instruction in arms. The Vrishnis and the Andhakas, and princes from various lands, and the (adopted) son of Radha of the Suta caste, (Karna), all became pupils of Drona. But of them all, the Suta child Karna, from jealousy, frequently defied Arjuna, and supported by Duryodhana, used to disregard the Pandavas. [/quote]
[quote]And seeing that in process of time his son had grown up, Adhiratha sent him to the city named after the elephant. And there Karna put up with Drona, for the purpose of learning arms. And that powerful youth contracted a friendship with Duryodhana. And having acquired all the four kinds of weapons from Drona, Kripa, and Rama, he became famous in the world as a mighty bowman. And after having contracted a friendship with Dhritarashtra's son, he became intent on injuring the sons of Pritha. And he was always desirous of fighting with the high-souled Falguna. And, O king, ever since they first saw each other, Karna always used to challenge Arjuna, and Arjuna, on his part, used to challenge him.[/quote]
So from the above, its clear that Karna also studied under Dronacharya.