Question

how many ways are there to distribute 15 distinct objects into 5 distinct boxes with: at least three empty box.and no empty box.

Answer 1

1. With 3 box3s left : There are two boxes left, so we will be dividing 15 objects into 2 parts. The half of 15 is 7.5 but we cannot do that because we can't divide one object into two halves, so, we can keep 8 objects in 1 box and 7 objects in 2nd box.
2. With no boxes left : There are 15 objects and 5 boxes, so we have to divide them 3 each in a box because 15/5=3.


Hope this helps!