回复：我认为，您的第一题答案是正确的。

The answer to the 2nd question should be correct as well. We can think the 2nd question as this:

Put 20 balls in 5 bins, which has two scenarios: 1. none of the five bins can be empty, which results in C(19,4); 2. the fifth bin is empty, which results in C(19,3). Therefore, the total number is C(19,4)+C(19,3)=C(20,4).