The notation \( P(10, 10) \) represents a **permutation**, specifically the number of ways to arrange 10 objects taken all 10 at a time.

The formula for permutations is given by:

\[
P(n, r) = \frac{n!}{(n - r)!}
\]

In this case, \( n = 10 \) and \( r = 10 \). So,

\[
P(10, 10) = \frac{10!}{(10 - 10)!} = \frac{10!}{0!}
\]

Since \( 0! = 1 \), this simplifies to:

\[
P(10, 10) = 10!
\]

Now, calculating \( 10! \):

\[
10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3,628,800
\]

So, \( P(10, 10) = 3,628,800 \).

### Summary:
The value of \( P(10, 10) \) is **3,628,800**.

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Do you have any questions or need further details?

### Related Questions:
1. How does permutation differ from combination?
2. What is \( P(10, 9) \) and how is it calculated?
3. Can you explain when we use permutations in real-life scenarios?
4. How does factorial notation work, and what are its properties?
5. What is the difference between \( P(n, r) \) and \( C(n, r) \)?

### Tip:
Permutations are used when **order matters** in arranging objects, while combinations are used when the order does **not** matter.

Learn how to calculate the permutation P(10, 10) using the factorial formula. This problem involves arranging 10 objects in 10 positions, with a detailed step-by-step breakdown of the process. Suitable for students in Grades 9-12.

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