number of possibilities to interview students One semester includes 13 weeks, Given 8 students we want to interview them with the following conditions:

1) Each student should be interviewed at least once.

2) None can be interviewed more than 3 times (3 is the maximum).

Calculate the number of possibilities to interview the students.

Note: As usual, the order of interviews matters so interviewing A at the first week and B at the second is not the same as interviewing B at the first and A at the second week.
Hint: Split by cases.    


   Each student has to be interviewed once, so how can the remaining 5 interviews be done? It has to be either $1+1+1+1+1$, $1+1+1+2$, or $1+2+2$.


Can you take it from here?
After getting Hint here's my suggested answer, hope someone can review it: