Question: 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, child 2 gets 0 apples, child 3 gets 2 apples, child 4 gets 0 apples, child 5 and child 6 get 1 apple each, and child 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 1 apple.)
b. How many distributions are possible if each child is to receive at least 1 apple?