How many ways can you distribute 10 identical balls into two non identical boxes so none are empty?

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?

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