The mathematical expression provided is $P^9_2$, which represents a permutation. The formula for permutations is:

$P^n_r = \frac{n!}{(n-r)!}$

Here, $n = 9$ and $r = 2$. Let's calculate it:

$P^9_2 = \frac{9!}{(9-2)!} = \frac{9!}{7!}$

Expanding the factorials:

$P^9_2 = \frac{9 \times 8 \times 7!}{7!}$

Cancel $7!$:

$P^9_2 = 9 \times 8 = 72$

Thus, $P^9_2 = 72$.

Would you like more details or have any questions?

Related Questions:

1. What is the formula for combinations and how does it differ from permutations?
2. Can you explain why the order of selection matters in permutations?
3. How would $P^n_r$ change if $r > n$, and why is it undefined?
4. Can we calculate $P^n_r$ directly using a calculator, and how?
5. How do permutations apply to real-life problems, such as arranging people in a line?

Tip:

When dealing with permutations, remember that the order of arrangement is important—this distinguishes it from combinations!