In how many ways can you distribute $$10$$ identical balls, into two non-identical boxes so that none are empty? A $$2$$B $$8$$C $$9$$D $$10$$
$$(1,9),(2,8),(3,7),(4,6),(5,5),(6,4),(7,3),(8,2),(9,1)$$ In 9 ways 10 identical balls into two boxes can be distributed.
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In how many ways can I distribute $100$ identical balls into $6$ different boxes so that no box is left empty and every box contains even number of elements? Firstly, I placed $2$ balls in every box, which covers the condition that no box is left empty and since they all have to contain even number of elements I chose $2$ balls. Now there are $88$ balls left which I have to distribute. I just don't know how to cover the condition that every box should have even number of elements? Can I for example, look at two balls as "one" ball, and distribute the "$44$" balls into $6$ boxes? Then I could use Stirling number of the second kind... $\endgroup$ |