The expression $P(4, 3)$ refers to the permutation of 4 objects taken 3 at a time. The formula for permutations is:

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

Here, $n = 4$ and $r = 3$. Substituting these values into the formula:

$P(4, 3) = \frac{4!}{(4 - 3)!} = \frac{4!}{1!}$

Now, calculate $4!$ and $1!$:

$4! = 4 \times 3 \times 2 \times 1 = 24$ $1! = 1$

Thus:

$P(4, 3) = \frac{24}{1} = 24$

So, $P(4, 3) = 24$.

Would you like further explanation on permutations, or any other details?

Here are 5 related questions:

1. What is the difference between permutations and combinations?
2. How do you calculate $P(6, 2)$?
3. How does the factorial function work in permutation calculations?
4. What is the formula for combinations $C(n, r)$?
5. Can you explain real-world applications of permutations?

Tip: Permutations are used when the order matters, while combinations are used when order does not matter.