I have 168 people, they can pick from these set number

Mondays 95 days-off

Tueday 34 days-off

Wednesday 33 days-off

Thursday 33 days-off

Friday 33 days-off

Saturday 66 days-off

As of now I do a manual count at a certian point, and repeat this several times just not to end up with the problem I described above. Can someone please help?