The expression "blank subscript 12 end subscript P subscript 2 end subscript" seems to refer to a permutation notation, typically written as ${}^{12}P_2$. This represents the number of ways to select and arrange 2 objects from a set of 12 objects.

The formula for permutations, where $n$ is the total number of objects and $r$ is the number of objects to arrange, is given by:

${}^{n}P_{r} = \frac{n!}{(n-r)!}$

For $n = 12$ and $r = 2$:

${}^{12}P_2 = \frac{12!}{(12-2)!} = \frac{12!}{10!}$

Now, we calculate $12!$ and $10!$:

$12! = 12 \times 11 \times 10!$

$\frac{12!}{10!} = \frac{12 \times 11 \times 10!}{10!} = 12 \times 11 = 132$

Therefore, the value of ${}^{12}P_2$ is 132.

Answer:

132

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions to explore further:

1. What is the formula for combinations, and how does it differ from permutations?
2. How would you calculate ${}^{15}P_3$?
3. What is the difference between permutations with repetition and without repetition?
4. How can permutations be applied in real-life scenarios?
5. How do you calculate permutations when given constraints?

Tip: Remember, permutations