The notation \( P(18, 11) \) refers to a **permutation**. It represents the number of ways to arrange 11 objects chosen from a set of 18 distinct objects, where order matters. The formula for permutations is:

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

Here, \( n = 18 \) and \( r = 11 \). Applying the formula:

\[
P(18, 11) = \frac{18!}{(18 - 11)!} = \frac{18!}{7!}
\]

Now, calculating:

\[
18! = 18 \times 17 \times 16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7!
\]

Since the \( 7! \) terms cancel out, we are left with:

\[
18 \times 17 \times 16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8
\]

Let me calculate this for you.

The value of \( P(18, 11) \) is \( 1,270,312,243,200 \).

Would you like more details or have any questions about permutations?

Here are 5 related questions to expand on this topic:
1. How does a permutation differ from a combination?
2. What would \( P(18, 11) \) represent in a real-world context?
3. How can the concept of permutations be used in probability problems?
4. How does the formula for permutations change when some objects are identical?
5. What is the value of \( P(10, 5) \)?

**Tip:** In permutations, the order of selection matters, while in combinations, it does not.

Explore the concept of permutations and learn how to calculate P(18, 11). This detailed solution includes step-by-step calculations using the permutation formula, essential for students in Grades 10-12 studying combinatorics.

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