It looks like you are asking for the value of the permutation \( P(8,6) \). 

The formula for permutations is given by:

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

For \( P(8, 6) \), this becomes:

\[
P(8, 6) = \frac{8!}{(8 - 6)!} = \frac{8!}{2!}
\]

Now, let’s calculate this step by step:

1. \( 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320 \)
2. \( 2! = 2 \times 1 = 2 \)
3. Now, divide the two results: \( \frac{40320}{2} = 20160 \)

So, \( P(8, 6) = 20,160 \).

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the difference between permutations and combinations?
2. How would \( P(8, 3) \) be calculated?
3. Can you explain why \( P(n, n) \) equals \( n! \)?
4. How do permutations apply in real-life scenarios, such as seating arrangements?
5. What is the value of \( C(8,6) \), the combination of 8 items taken 6 at a time?

**Tip:** Permutations are used when the order of items matters, unlike combinations where the order doesn't matter.

Discover how to calculate the permutation P(8,6) using the formula P(n, r) = n! / (n - r)!. This detailed solution walks through each step of the process, including factorial calculations. Perfect for high school students in Grades 9-12 looking to master permutation concepts.

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