Simplify the expression.
12P5 (by the way numbers are smaller)
A. 11,880
B. 95,040
C. 1,235,520
D. 7,920
well, just multiply it out:
12*11*10*9*8
To simplify the expression 12P5, we can use the formula for permutation, which is given by:
nPm = n! / (n-m)!
In this case, we want to calculate 12P5, so we have:
12P5 = 12! / (12-5)!
First, let's calculate the factorial of 12.
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Next, let's calculate (12-5)!:
(12-5)! = 7!
Now, let's substitute these values back into the original formula:
12P5 = (12!) / (7!)
To simplify further, we need to calculate the factorial of 7:
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
Now, we can substitute this value back into the expression:
12P5 = (12!) / (7!) = (12 x 11 x 10 x 9 x 8) / (7 x 6 x 5 x 4 x 3 x 2 x 1)
Calculating this expression gives us:
12P5 = 95,040
Therefore, the correct answer is B. 95,040.