Evaluate the following expression.
_(6)P_2 =
I you mean 6P2 , then
= 6!/4!
= 6x5
= 30
To evaluate the expression _(6)P_2, we need to understand what the expression represents.
The notation _(n)P_r represents the number of permutations of r objects chosen from a total of n objects, where the order matters and repetition is not allowed. In other words, it gives us the number of ways we can arrange r objects out of a set of n objects.
To calculate _(6)P_2, we need to substitute the values of n and r into the formula:
_(n)P_r = n! / (n-r)!
n! represents the factorial of n, which is the product of all positive integers less than or equal to n.
For _(6)P_2:
n = 6
r = 2
Now let's calculate it step by step:
Step 1: Calculate n!
n! = 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Step 2: Calculate (n-r)!
(n-r)! = (6-2)! = 4! = 4 x 3 x 2 x 1 = 24
Step 3: Substitute the values into the formula and solve:
_(6)P_2 = n! / (n-r)!
= 720 / 24
= 30
Therefore, _(6)P_2 equals 30.