In this question, there are 5 identical apples and 6 identical oranges to be distributed.  
(a) How many ways are there to distribute the fruit among 4 children? ①(b) How many ways are there to do this if each child needs to receive at least one orange and notall of the fruit is required to be handed out?
(c) How many ways are there to distribute the fruit among 3 children such that no child receivestwo different types of fruit?②
(d) How many ways are there to lay the fruit in 3 piles? The piles must not be empty but it doesn’tmatter which pile is which.
(e) If one of the 3-pile arrangements from part (d) is chosen uniformly at random, what is theprobability that each pile consists of only one type of fruit?

① It is allowed for some child or children to receive nothing.
②Again, it is allowed for some child or children to receive nothing.

5个相同的苹果和6个相同的橘子待分发
（a）分给4个孩子有多少不同的分法？（①允许有的孩子什么都没分到）
（b）如果每个孩子至少分到一个橘子，不要求所有水果全部发完，一共有多少种分法？
（c）如果使每个孩子都没有分到两种不同的水果，一共有多少种分法？
（d）如果把水果分成三堆（堆与堆之间没有区别），每一堆都不是空的，一共有多少种分法？
（e）在按照（d）分好的水果中，随机挑选一种可能，三堆中每一堆都只有一种水果的概率是多少？

前三问已经解决，后两问实在解不出，向各位大神求助
（第四问中按全部排列组合出来的方法得到了一个结果，是83，不知正误也不懂解法，求指点）