On Halloween, 10 identical apples are distributed to 7 children. 

a. How many distributions are possible?

(Hint:One possible distribution is that child #1 gets 3 apples, #2 gets 0 apples, #3 gets 2 apples,#5and #6 get 1 apple each, and #7 gets 3 apples. Although the problem says apples are distributed to children, think of assigning a child"s name to each apple; a child"s name can go to more than one apple.) 

b. How many distributions are possible if each child is to receive at least one apple?

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