The notation \( P(8, 2) \) represents a permutation, specifically the number of ways to arrange 2 items from a set of 8 distinct items. This can be calculated using the formula for permutations:

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

In this case, \( n = 8 \) and \( r = 2 \), so:

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

Now, let's compute it step-by-step:

1. Calculate \( 8! \) up to the point we need:
   \[
   8 \times 7 = 56
   \]

2. This gives:
   \[
   P(8, 2) = 56
   \]

### Final Answer:
\[
P(8, 2) = 56
\]

Would you like additional details or have any questions?

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Here are 5 related questions you might find interesting:
1. What is the difference between permutations and combinations?
2. How would you evaluate \( P(10, 3) \)?
3. Can you explain how \( P(n, r) \) changes as \( r \) increases for a fixed \( n \)?
4. What is the formula for combinations, and how does it compare to the formula for permutations?
5. How can we interpret \( P(n, n) \) in practical scenarios?

**Tip:** Remember, permutations consider the order of selection, while combinations do not.

Learn how to evaluate the permutation P(8, 2) using the factorial formula for permutations, with a step-by-step solution. This problem introduces key concepts in combinatorics, including factorials and permutations, making it suitable for students in Grades 9-10.

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