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The question asks us to find the number of ways to distribute 4 storybooks and 3 poem books among 3 children, given that each child receives at least one book of each type.

### Step-by-Step Solution:

1. **Distributing Storybooks:**
   We have 4 identical storybooks and need to distribute them among 3 children such that each child gets at least one storybook. This can be solved using the "stars and bars" method, ensuring no child gets zero books.

   - First, give 1 storybook to each child. This uses up 3 storybooks, leaving 1 storybook to distribute.
   - The number of ways to distribute 1 remaining storybook among 3 children is simply 3 (each child can get the extra book).

2. **Distributing Poem Books:**
   Similarly, we have 3 identical poem books and want to distribute them among 3 children, ensuring each child receives at least one book.
   
   - Give 1 poem book to each child, using up all 3 books.
   - There is only 1 way to distribute these 3 books such that each child gets exactly 1 book.

3. **Calculating the Total Number of Ways:**
   The total number of ways is obtained by multiplying the number of ways to distribute storybooks by the number of ways to distribute poem books:

   \[
   3 \text{ (storybook ways)} \times 1 \text{ (poem book ways)} = 3
   \]

So, the total number of ways to distribute these books among the 3 children is **3**.

**Answer: 3**

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Would you like more details or have any questions? Here are 5 related questions for further practice:

1. How many ways can we distribute 5 identical items among 4 people if each person receives at least one item?
2. If there are 6 identical apples and 4 children, how many ways can we distribute the apples so that each child gets at least one apple?
3. How many ways can you distribute 10 identical balls among 3 children with no restrictions?
4. What is the number of ways to distribute 7 identical storybooks and 4 identical poem books among 3 children if each child must receive at least one book?
5. How many ways are there to distribute 5 different books among 3 children, with no restrictions?

**Tip:** When distributing identical items among a group with restrictions, consider the "stars and bars" method combined with initial allocations to meet minimum requirements.

There are 4 storybooks of the same type and 3 poem books of the same type. In how many ways can we distribute these books among three children? (Every child has received at least one book of each type.)

Learn how to distribute 4 storybooks and 3 poem books among 3 children, ensuring each child receives at least one book of each type. The problem uses the stars and bars method and is suitable for high school students in Grades 9-12.

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