The notation $8P3$ refers to a permutation problem, where we want to determine the number of ways to arrange 3 objects out of 8 distinct objects. The formula for permutations is:

$nP_r = \frac{n!}{(n - r)!}$

In this case, $n = 8$ and $r = 3$, so we have:

$8P3 = \frac{8!}{(8 - 3)!} = \frac{8!}{5!}$

Now, calculate $8!$ and $5!$:

$8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320$ $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

Now, divide the two values:

$8P3 = \frac{40320}{120} = 336$

So, $8P3 = 336$.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. What is the difference between permutations and combinations?
2. How would you solve $8C3$ (combinations)?
3. How is the formula for permutations derived?
4. How can you apply permutations to real-world problems?
5. What happens if all objects are identical? How does that affect permutations?

Tip: For larger numbers, using factorial functions on a calculator can save time when computing permutations.