Question

How many ways are there to distribute 10 district objects into 4 distinct boxes with: i) At least two empty box. ii) No empty box

Answer 1

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Option #1: two boxes with 5 balls.
we need to choose them, then divide the 10 balls into 2 group of 5 balls each, the order inside the boxes does not matter.


Option #2: only one box with 5 balls, choose 1 box to have 5 balls, choose 5 balls for the box, now divide rest of balls but subtract 3 options where all balls went to the same box.



If one box holds 5 balls, the other 3 must hold the remaining 5.
There are 3 ways for them to be distributed 5-0-0
There are 6 ways for them be be distributed 4-1-0
There are 3 ways for them be be distributed 3-1-1
There are 3 ways for them be be distributed 2-2-1
The answer is 15.:-) ------


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