1. Choose the books for Alexandria:
* Alexandria gets 3 books. We need to choose 3 books out of 7. This can be done in ⁷C₃ ways, which is 7!/(3!4!) = 35 ways.
2. Distribute the remaining books:
* There are 4 books left. These need to be distributed between Robin and Lily. Since we don't care about the order they receive the books, we can think of it like this:
* Robin can get 0, 1, 2, 3, or 4 books.
* For each of these possibilities, the rest go to Lily.
3. Calculate the possibilities for Robin and Lily:
* Robin gets 0 books: There's only 1 way this can happen.
* Robin gets 1 book: There are 4 ways to choose which book Robin gets.
* Robin gets 2 books: There are ⁶C₂ = 15 ways to choose which 2 books Robin gets.
* Robin gets 3 books: There are ⁴C₃ = 4 ways to choose which 3 books Robin gets.
* Robin gets 4 books: There's only 1 way this can happen.
4. Multiply the possibilities:
* We need to multiply the number of ways to choose books for Alexandria by the number of ways to distribute the remaining books:
35 (ways to choose for Alexandria) * (1 + 4 + 15 + 4 + 1) (ways to distribute the rest) = 35 * 25 = 875
Therefore, there are 875 ways to distribute the 7 books so that Alexandria gets 3.