A teacher bought 20 apples. She wants to distribute the apples to 5 children. However, she decides to keep 7 apples for herself. (a) How many different ways can she distribute the remaining apples to the 5 children? (b) How many different ways can she distribute the remaining apples to the 5 children if each child receives at least 2 apples? (c) How many different ways can she distribute the remaining apples to the 5 children if each child receives at most 3 apples?

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