PERFORM THE INDICATED CALCULATIONS
5P2/12P4
To perform the calculations of 5P2 / 12P4, we will first calculate the values of both permutations.
Permutation is calculated using the formula nPr = n! / (n - r)!, where n represents the total number of items and r represents the number of items being selected.
Let's calculate each permutation step-by-step:
1. 5P2 = 5! / (5 - 2)!
= 5! / 3!
= (5 * 4 * 3!) / 3!
= (5 * 4) / 1
= 20
2. 12P4 = 12! / (12 - 4)!
= 12! / 8!
= (12 * 11 * 10 * 9 * 8!) / 8!
= (12 * 11 * 10 * 9)
= 11,880
Now, we can calculate the expression 5P2 / 12P4:
5P2 / 12P4 = 20 / 11,880
Therefore, the final result is 20 / 11,880.
To perform the indicated calculations, we need to understand what 5P2 and 12P4 represent.
Here, the notation "nPm" represents the permutation of n objects taken m at a time, which can be calculated using the formula:
nPm = n! / (n - m)!
Where "!" denotes the factorial function, which means multiplying a number by all the positive integers less than it down to 1.
Let's calculate each term step by step:
1. Calculating 5P2:
- First, calculate the factorial of 5: 5! = 5 * 4 * 3 * 2 * 1 = 120
- Then, calculate the factorial of (5 - 2): (5 - 2)! = 3! = 3 * 2 * 1 = 6
- Now, divide 5! by (5 - 2)!: 5P2 = 120 / 6 = 20
2. Calculating 12P4:
- First, calculate the factorial of 12: 12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
- Then, calculate the factorial of (12 - 4): (12 - 4)! = 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
- Now, divide 12! by (12 - 4)!: 12P4 = (12 * 11 * 10 * 9) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
Thus, to perform the calculation, divide 5P2 by 12P4:
5P2 / 12P4 = 20 / (12 * 11 * 10 * 9) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
It is important to note that due to the extensive calculations involved, it is necessary to use a scientific calculator or software capable of handling large factorials.
First, please do not use all capitals. Online it is like SHOUTING. Not only is it rude, but it is harder to understand. Thank you.
Second, I don't understand what calculations are indicated. However, if you mean:
(5p^2)/(12p^4) = 5/12p^-2
Online "^" indicates "to the power of."