Pigeonhole Principle & Code Golf
Mathematica, 68 bytes

Print/@(10^RandomSample@RandomChoice[IntegerPartitions[+##,{#}]-1])&amp;


An unnamed function that takes two integer arguments, the number of boxes, followed by the number of items.

It first computes all possible partitions of N+M into exactly M positive parts, and subtracts 1 from each partition afterwards. This gives us all possible partitions of N into M non-negative parts (which IntegerPartitions wouldn't generate otherwise). Then pick a random partition and shuffle it. This guarantees all possible ordered partitions with zeros are allowed. Finally, convert each bin of the partition to an output line by raising 10 to the corresponding power (such that each line becomes 1000... with k zeros). An example output might look like:

100
10000
1
10
10