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. 
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.) 
Options:
$$2$$ 
$$3$$ 
$$4$$ 
$$10$$ 