https://file.aiquickdraw.com/mathbot/file/1726853679524xrn5hqqd.jpg

The question in the image asks: 

**"Wie viele Möglichkeiten gibt es, 6 unterscheidbare Geschenke auf 6 Kinder so zu verteilen, dass keines dieser Kinder leer ausgeht?"**

Translation:

**"How many ways are there to distribute 6 distinguishable gifts to 6 children so that none of the children goes empty-handed?"**

This problem is essentially asking for the number of ways to assign 6 distinct gifts to 6 distinct children, where each child receives exactly one gift. This is a classical problem of **permutations**.

The number of ways to assign \(n\) distinct objects to \(n\) distinct recipients is given by \(n!\) (n factorial), which represents the total number of permutations.

For \(n = 6\), we calculate:

\[
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720
\]

Thus, the number of ways to distribute 6 distinguishable gifts to 6 children is **720**.

Would you like further details on the concept or any additional questions?

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Here are 5 related questions:

1. What is the formula for calculating the number of ways to distribute \(n\) distinguishable objects to \(n\) recipients?
2. How would the solution change if there were more children than gifts?
3. What if the gifts were not distinguishable? How would that affect the solution?
4. How can this problem be extended to more complex scenarios, like allowing some children to receive multiple gifts?
5. What are permutations and how do they differ from combinations?

**Tip:** Whenever dealing with distributions where no one is left empty-handed, permutations are a powerful tool!

Wie viele Möglichkeiten gibt es, 6 unterscheidbare Geschenke auf 6 Kinder so zu verteilen, dass keines dieser Kinder leer ausgeht?

Learn how to calculate the number of ways to distribute 6 distinct gifts to 6 children using permutations. This problem covers key mathematical concepts such as factorials and permutations. Suitable for high school students.

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