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!