Discrete Mathematics
# Distribution into Bins

Indy, Allan, and Nathan have found 8 identical rubies. How many ways are there to distribute the treasure among the adventurers?

**Note**: Some distributions might have some adventurers receiving zero rubies.

There are 6 distinct fish in an aquarium. 12 identical food pellets are spread on the top of the tank.

How many distributions of food pellets are there in which at least one fish *does not* receive a food pellet?

There are 9 distinct people (including the host) at a party. The host orders two 12-cut pizzas (24 identical pizza slices in total).

How many distributions of pizza slices are there such that each person receives *at least* 2 slices?

At a newspaper headquarters, there are 5 distinct journalists and 13 assignments to be distributed among them. Each assignment will take any of the journalists the same amount of time to complete.

How many distributions of assignment *times* are there if each journalist gets at least one assignment?