If all the balls fall into one bin, according to Probability Theory it's just as
likely as any other outcome, but it doesn't make us feel good that our assumption that
each bin was equally likely was correct.
Likewise, if each bin ends up with exactly the same number of balls it should
also make us feel bad. In this case each throw is probably not independent of all previous
throws.
Interesting Paradoxes of Probability are covered at