The Mathematics Department at Sun Tan University is sending a delegation of mathematicians and graduate students to a conference. They will pay for 4 mathematicians and 5 graduate students to go. If the department has 16 mathematicians and 24 graduate students, how many different delegations are possible?

The mathematicians at Sun Tan University have published 14 research papers this year. The department chair wants to display them in the lobby. The display case can show 4 at a time. How many arrangements of 4 research papers are possible?