I have 6 distinguishable balls I want to put into 4 distinguishable boxes stacked on top of each other. The restriction is that the lower box must contain at least one, and the upper box must contain exactly one.
My solution is: there are 6 different ways to fill the upper box. after that, there are 5 different ways to fill the lower box. after that, the third ball can be put into 3 boxes (i.e. all but the upper one), and so on for the fourth, fifth and sixth balls. so my solution is: $6 * 5 (3 * 3 * 3 * 3) $
Am I correct? I've searched so much for such problems and couldn't understand most of the answers. My knowledge is limited to factorials, n choose k, permutations and complementary events.