Day 1: Partridges in a Pear Tree
The partridge host has prepared 12 pears to serve. She does not eat any pears. However her 7 guests are quite particular:
- Every guest must have at least one pear.
- Two of the guests are particularly important, so they both must have at least two pears.
- No guest may have four or more pears (otherwise they will feel insulted for being greedy).
How many ways are there to distribute all the pears?
All the guests are distinguishable (so order matters) and yes, all the pears are served (whole).