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.

Learn how to evaluate the permutation P(4, 3) with a detailed explanation and step-by-step calculation using the permutation formula. Understand the use of factorials in combinatorics. Suitable for students in Grades 9-12.

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