The notation \( 6P2 \) represents a **permutation**, which calculates the number of ways to arrange 2 objects from a set of 6 distinct objects.

The formula for permutations is:

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

Where:
- \( n = 6 \)
- \( r = 2 \)

Substituting the values into the formula:

\[
6P2 = \frac{6!}{(6-2)!} = \frac{6!}{4!}
\]

Now, calculate the factorials:
- \( 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \)
- \( 4! = 4 \times 3 \times 2 \times 1 = 24 \)

Thus:

\[
6P2 = \frac{720}{24} = 30
\]

So, \( 6P2 = 30 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the difference between permutations and combinations?
2. How do you calculate \( nCr \) (combinations)?
3. How does the formula change for permutations with repetition allowed?
4. Can you explain when to use permutations versus combinations?
5. What is \( 6P3 \) and how does it compare to \( 6P2 \)?

**Tip:** When calculating permutations, order matters—always keep this in mind when deciding whether to use permutations or combinations!

Discover how to calculate the permutation 6P2 using the formula nPr = n! / (n - r)!. This problem involves understanding factorials and arranging objects, making it suitable for students in Grades 9-12. Includes a step-by-step solution to find that 6P2 equals 30.

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