I'm not sure if this is the correct subforum to post this question to, but I would really like some help with this combinatorics/distribution question:
I am trying to understand whether it is possible to group 62 people into 3 groups with some requirements:
Group A is 10 people
Group B 26
Group C 26
Every day 62 people will go out for dinner. But it will be in these 3 different groups. And they will go to different restaurants. These groups will go to dinner 6 times in total, and there is a list of 6 different restaurants any group can choose to go to.
The requirements, and I would like to see whether this is possible are as follows:
I am trying to understand whether it is possible to group 62 people into 3 groups with some requirements:
Group A is 10 people
Group B 26
Group C 26
Every day 62 people will go out for dinner. But it will be in these 3 different groups. And they will go to different restaurants. These groups will go to dinner 6 times in total, and there is a list of 6 different restaurants any group can choose to go to.
The requirements, and I would like to see whether this is possible are as follows:
- Can we ensure that 60 people (out of the whole 62) will join group A for dinner at least once? I am aware that this would mean that it must be 10 completely different people each night on that group.
- Also ensure that everyone can visit all 6 restaurants?
- Ensure that groups do not repeat? (If even one person is different in a group, then that's fine)