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.