The expression $8P2$ represents the number of permutations of 8 items taken 2 at a time. The formula for permutations is:

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

In this case:

• $n = 8$
• $r = 2$

So,

$8P2 = \frac{8!}{(8 - 2)!} = \frac{8!}{6!}$

Calculating this:

$8! = 8 \times 7 \times 6! = 56 \times 6!$

Thus,

$\frac{8!}{6!} = 56$

So, $8P2 = 56$.

Would you like a deeper explanation or have any questions?

1. What are permutations, and how do they differ from combinations?
2. How does factorial notation work in permutations?
3. Can $8P2$ be calculated without factorials?
4. How would $8C2$ differ from $8P2$?
5. How do permutations apply to real-life situations?

Tip: Permutations focus on arrangements where order matters.