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 a 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?

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