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Nini has $$6$$ identical balls and she wants to place them into $$3$$ identical baskets. How many different ways can she do so? (The baskets cannot be empty.) 
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Since the balls and baskets are all identical, the order does not matter.  $$6=1+1+4$$  $$6=1+2+3$$  $$6=2+2+2$$  So, there are $3$ ways to place them. 