Question
Find the value of the permutation. 4P3
Find the value of the permutation
The Correct Answer and Explanation is:
Answer:
The value of the permutation 4P3 is 24.
Explanation
A permutation refers to an arrangement of objects in a specific order. The notation nPr represents the number of permutations of r items selected from a total of n distinct items, where order matters.
The formula to calculate a permutation is: nPr=n!(n−r)!nP_r = \frac{n!}{(n – r)!}
Where:
- n! (n factorial) is the product of all positive integers up to n.
- (n – r)! is the factorial of the difference between n and r.
Let’s apply this to 4P3: 4P3=4!(4−3)!=4!1!4P_3 = \frac{4!}{(4 – 3)!} = \frac{4!}{1!}
First, calculate the factorials:
- 4! = 4 × 3 × 2 × 1 = 24
- 1! = 1
So: 4P3=241=244P_3 = \frac{24}{1} = 24
This means there are 24 different ways to arrange 3 items out of a set of 4 when the order of selection matters.
Understanding Through an Example:
Suppose you have 4 people: A, B, C, and D. You want to assign 3 of them to 3 different positions: President, Vice President, and Secretary. Since the positions are different, the order in which you assign them matters.
Let’s look at a few possibilities:
- A, B, C
- A, C, B
- B, A, C
- B, C, A
- C, A, B
- C, B, A
… and many more, totaling 24 unique ordered arrangements.
If the order did not matter (e.g., combinations), there would be fewer arrangements. But since order does matter in permutations, we count all the possible ways the items can be ordered.
Thus, 4P3 = 24, meaning 24 different permutations of 3 items chosen from 4.
