At a recruitment event, 34 candidates are interviewed by 4 groups of interviewers (each group consisting of 2 interviewers);

What is the probability of the following happening:

1. Only candidates (A and B) have the same group of interviewers (C and D);

**and**

2. A and B are given the same mark by C and D- 34/50;

**and**

3. The interview marking form used by C and D for A and B have been filled out incorrectly. All other forms by other pairs of interviewers have been filled out correctly for the other 32 candidates;

**and**

4. Interviewer C was involved in 8 other interviews and correctly filled out the interview marking form.

Can any boffins on here tell me how they would work out the chances of all this happening?

Many thanks!