To calculate 4P2, we need to understand what the notation means. “P” in this context stands for permutation, which refers to the number of ordered arrangements or selections we can make from a given set of objects. In this case, we have 4 objects from which we want to choose 2.
The formula for calculating permutations is nPr = n! / (n – r)!, where n is the total number of objects and r is the number of objects we want to choose.
Let’s break down the calculation step by step.
Step 1: Calculate the factorial of n.
Factorial refers to the product of an integer and all the positive integers below it. In this case, we need to calculate 4!.
4! = 4 x 3 x 2 x 1 = 24
Step 2: Calculate the factorial of (n – r).
In this case, n – r = 4 – 2 = 2. So, we need to calculate 2!.
2! = 2 x 1 = 2
Step 3: Divide the factorial of n by the factorial of (n – r).
NPr = 4! / 2!
= 24 / 2
= 12
Therefore, the answer to 4P2 is 12.
To better understand the concept, let’s consider a practical example. Imagine you have 4 different colored pens – red, blue, green, and black. You want to select 2 pens from this set.
Using the permutation formula, we can calculate the number of possible arrangements.
Step 1: Calculate the factorial of 4.
4! = 4 x 3 x 2 x 1 = 24
Step 2: Calculate the factorial of (4 – 2).
2! = 2 x 1 = 2
Step 3: Divide the factorial of 4 by the factorial of (4 – 2).
4P2 = 4! / 2!
= 24 / 2
= 12
So, there are 12 different ways to select 2 pens from the set of 4, considering the order in which they are chosen. For example, you could choose red and blue, blue and red, red and green, green and red, etc.
In summary, to calculate 4P2, we use the formula nPr = n! / (n – r)!, where n is the total number of objects and r is the number of objects we want to choose. By plugging in the values, we find that 4P2 is equal to 12.