Evaluate blank subscript 12 end subscript P subscript 2 end subscript?
78
132
210
564

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

Evaluate blank subscript 12 end subscript P subscript 2 end subscript?

Learn how to calculate the permutation 12P2 using the formula for permutations. This detailed explanation covers factorials and shows the calculation step-by-step, providing the final answer as 132. Suitable for students in Grades 9-12.

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