The expression \( P(n, 1) \) refers to a **permutation** of \( n \) objects taken 1 at a time. The formula for permutations is:

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

In this case, where \( r = 1 \), the formula simplifies to:

\[
P(n, 1) = \frac{n!}{(n - 1)!}
\]

Since \( n! = n \times (n - 1)! \), the expression further simplifies to:

\[
P(n, 1) = n
\]

This means that the number of ways to select 1 object from \( n \) objects is simply \( n \), as you're just choosing 1 item out of \( n \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the formula for \( P(n, r) \) in general?
2. How does the concept of permutations differ from combinations?
3. How would \( P(n, 2) \) be calculated?
4. How is the factorial function used in permutation problems?
5. What are some practical examples of permutations?

**Tip:** Always remember that order matters in permutations, but not in combinations.

Learn how to calculate permutations when selecting 1 object from n using the formula P(n, 1) = n. This solution explains the key concepts of permutations, factorials, and the general formula P(n, r). Suitable for students in Grades 9-12.

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