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.

Case 5

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

Case 6

Suppose Prof. Smith and his students Mr. A and Ms.B, submit 3 papers (P_①, P_②, P_③), and three of them attend the conference.

Case 7

Suppose Prof. Smith and his student Mr. A submit 1 paper (P_①), and only Mr. A attends the conference.

Case 8

Suppose that Prof. Smith and his student Mr. A submit 1 paper (P_①), and both of them attend the conference.

Case 9

Suppose that Prof. Smith and his Students A, B, C, and D, submit 4 papers (P-①,P-②,P-③,P-④) and five of them attend the conference, and Prof. Smith intends to pay all the expenses.