Case 1

Suppose that Prof. Smith and his student Mr. A submit 2 papers (P_① and P_②), and only Prof. Smith attends the conference.

Case 2

Suppose that Prof. Smith and his student Mr. A submit 2 papers (P_① and P_②), and both of them attend the conference.

Case 3

Suppose that Prof. Smith and his students Mr. A and Ms.B, submit 3 papers (P_①, P_②, P_③), and only Prof. Smith attends the conference.

Case 4

Suppose that Prof. Smith and his student Mr. A submit 3 papers (P_①, P_②, P_③) and both of them attend the conference, and Prof. Smith intends to pay for all 3 papers.