Question

How do you find the value of the permutation \[P\left( {4,2} \right)\] ?

Answer 1

Hint: Given is the permutation. We are given with the values of both n and r. we will directly use the formula to find the answer. Permutation is used to find the number of arrangements and selections in different cases.
Formula used:
\[{}^n{P_r} = \dfrac{{n!}}{{\left( {n - r} \right)!}}\]

Complete step-by-step answer:
Given that \[P\left( {4,2} \right)\].
Comparing it with \[P\left( {n,r} \right)\] we get \[n = 4,r = 2\]
Putting the values in the formula,
\[{}^4{P_2} = \dfrac{{4!}}{{\left( {4 - 2} \right)!}}\]
\[{}^4{P_2} = \dfrac{{4!}}{{2!}}\]
We know that \[4! = 24\] and \[2! = 2\]
Putting these values in the formula above we get,
\[{}^4{P_2} = \dfrac{{24}}{2}\]
On dividing the numbers we get,
\[{}^4{P_2} = 12\]
This is our answer.
So, the correct answer is “ \[{}^4{P_2} = 12\] ”.

Note: Here just note that value of r and n should be taken correctly. If they got interchanged the answer will be wrong. Also note that if n and r are equal then don’t write 0! As zero; it is actually one.
A permutation is said to be linear if the objects are arranged in a line.
A permutation is said to be circular if the objects are arranged in a circle.
A permutation of n dissimilar things taken r at a time can be written as \[{}^n{P_r}\] or \[P\left( {n,r} \right)\].