1. For the first one, I have considered toys to be different. When objects to be distributed are greater than the available persons and each should get at least one, we cannot do give one to each and then permute remaining anyhow. Here comes the concept of grouping and distribution.
2. The second one is the permutation of star and bars with extra criteria of having at least one from each. Take one from each which makes the equation as X' + Y' + Z' = 2 (Two stars and two bars)