Formula to determine number of questions required in 'pool'

We are seeking a calculation, formula or simulation to inform how many items/questions we require in an item bank or pool to facilitate ‘on-demand’ online testing for postgraduate examinations. This may suit a mathematician, psychometrician or statistician.

As an example, we may have 100 candidates sitting an examination comprising 100 multiple-choice questions. Each question is linked to a learning outcome, and each candidates’ paper must be balanced across learning outcomes. In addition, questions are tagged as ‘easy’, ‘moderate’ or ‘difficult’, and questions selected for each paper will need to be balanced across these levels (e.g. approximately 33 from each category).

Each candidate can see no more than 10% of questions seen by any other individual candidate (there is a second option for candidates to see no more than 25% of questions seen by any other individual candidate).

A calculation, formula or simulation that can be applied to variations of the above is required.