To evaluate \( 12P5 \), we use the formula for permutations, which is given by:
\[ nPr = \frac{n!}{(n - r)!} \]
Where:
- \( n \) is the total number of items,
- \( r \) is the number of items to choose.
In this case, \( n = 12 \) and \( r = 5 \).
So we calculate \( 12P5 \):
\[ 12P5 = \frac{12!}{(12 - 5)!} = \frac{12!}{7!} \]
Now, we can expand \( 12! \):
\[ 12! = 12 \times 11 \times 10 \times 9 \times 8 \times 7! \]
Thus, we have:
\[ 12P5 = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{7!} \]
The \( 7! \) cancels out:
\[ 12P5 = 12 \times 11 \times 10 \times 9 \times 8 \]
Now we calculate this step by step:
- \( 12 \times 11 = 132 \)
- \( 132 \times 10 = 1320 \)
- \( 1320 \times 9 = 11880 \)
- \( 11880 \times 8 = 95040 \)
Thus,
\[ 12P5 = 95040 \]
Therefore, the answer is:
A. 95,040