Python to solve combination problem (similiar to Kirkman's Schoolgirl Problem)

Job ID: 35627152

Budget: $12 – $30 SGD

Problem statement:
A given list of 20 candidates, 6 candidates in a group. Which groups (a list of groups) are best optimized to ensure all the candidates are well covered?

More than simple combinations, it is similar to the Kirkman's Schoolgirl Problem. Reference here:
1. https://stackoverflow.com/questions/56129886/how-to-use-z3-solver-to-solve-kirkman-s-schoolgirl-problem
2. https://stackoverflow.com/questions/60385092/split-array-to-sub-arrays-5-times-while-keeping-unique-pairs-in-all-sub-arrays
3. https://cs.lmu.edu/~ray/notes/kirkman/

The current solution I'm using is not Python. (No idea how it is calculated and produce.) Given 20 candidates, 6 in the group. It gives a solution of about 2000 groups.

I'm looking for a similar or even better solution in Python.

Note: the number of inputs needs to be flexible, such as 15 candidates to 25 candidates.

Thank you.
Related categories: Python Statistics Mathematics Operations Research