Simplify each expression. 8P5
8P5 ----> found on your calcualtor
= P(8,5) ----> found on some Calculators
= = 8!/3!
= 6720
To simplify the expression 8P5, we need to understand what the expression represents. The notation "nPm" denotes the number of permutations of "n" objects taken "m" at a time. In other words, it represents the number of ways we can arrange "m" objects from a set of "n" objects where order matters and repetitions are not allowed.
In this case, 8P5 represents the number of ways we can arrange 5 objects from a set of 8 objects.
To calculate the value of 8P5, we can use the formula for permutations:
nPm = n! / (n - m)!
Here, "n!" denotes the factorial of "n" which is the product of all positive integers less than or equal to "n".
So, for 8P5, we have:
8P5 = 8! / (8 - 5)!
Calculating the factorials:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
(8 - 5)! = 3!
Simplifying further:
8P5 = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1)
8P5 = 8 x 7 x 6 = 336
So, the simplified expression 8P5 is equal to 336.