To evaluate \( ¹²p⁵ \), we use the formula for permutations. The formula for permutations is given by:
\[ _nP_r = \frac{n!}{(n-r)!} \]
Where:
- \( n \) is the total number of items,
- \( r \) is the number of items to choose.
In this case, \( n = 12 \) and \( r = 5 \). Therefore, we need to calculate \( ¹²p⁵ \):
\[ ¹²p⁵ = \frac{12!}{(12-5)!} = \frac{12!}{7!} \]
Now, we can simplify \( \frac{12!}{7!} \):
\[ ¹²p⁵ = 12 \times 11 \times 10 \times 9 \times 8 \]
Calculating that step by step:
- \( 12 \times 11 = 132 \)
- \( 132 \times 10 = 1320 \)
- \( 1320 \times 9 = 11880 \)
- \( 11880 \times 8 = 95040 \)
Thus, \( ¹²p⁵ = 95040 \).
So the answer is:
A. 95,040