Evaluate the quantity.
P(10,4)
10!/ (10-4)! = 10!/6! = 10 * 9 * 8 * 7 = 5040
To evaluate the quantity P(10,4), we can use the formula for permutations.
The formula for permutations is:
P(n, r) = n! / (n - r)!
where n is the total number of items and r is the number of items chosen or arranged.
In this case, n = 10 and r = 4.
So, we can substitute the values into the formula:
P(10, 4) = 10! / (10 - 4)!
Now let's calculate the factorial part:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Since we only want the factorial up to (10 - 4) = 6, we can write the calculation as:
10! / 6!
Now, we can simplify the expression:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Substituting these values into the expression:
P(10, 4) = 3,628,800 / 720
P(10, 4) = 5,040
Therefore, P(10, 4) is equal to 5,040.
To evaluate the quantity P(10,4), we need to determine the value of the permutation function with n = 10 and r = 4.
The permutation function, denoted as P(n, r), calculates the number of ways to arrange r objects from a set of n distinct objects, considering the order of arrangement.
The formula to calculate permutations is:
P(n, r) = n! / (n - r)!
Where "!" denotes the factorial function, which means multiplying a number by all positive integers less than it down to 1.
Let's calculate P(10, 4) step by step:
1. Calculate the factorial of 10:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
2. Calculate the factorial of (10 - 4):
(10 - 4)! = 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
3. Divide the factorial of 10 by the factorial of (10 - 4):
P(10, 4) = 10! / (10 - 4)! = 3,628,800 / 720 = 5,040
Therefore, the value of P(10, 4) is 5,040.