Creating a seating plan

Question

I am running a one week (7 Day) program for 35 people. Each day there will be 5 programs, So 7 people in each program group each day. I want to ensure that each of the 35 people will be able to meet and work together in one program at least once during the 7 days.

is there an easy way to work out a seating plan for this.. Please help :)

Answer 1

So the best answer to solve this problem is to provide break down the 35 people in each of the 5 programs which means 7 of 35 people will be in each program.

First you need to consider that order does matter on the programs to make sure they get to the them at least once but then the people will be repeating two programs twice on two of the seven days.

It starts as permutation where order matters for the first 5 days then last 2 a combination where order does not matter

Try to consider and find the number of ways we can group the people in the programs together and let me know how that helps and we can continue from there?