Question

What does ${}^{n}{{P}_{r}}$ mean in math?

Answer 1

Hint: To give an answer to this question first we will recall the definitions of the permutations and combinations. Then by discussing the properties, differences between permutation and combination and analyzing the formulas of both we get the desired answer.

Complete step by step solution:
We have to find the meaning of ${}^{n}{{P}_{r}}$ in math.
Now, we know that in math we have two concepts named permutation and combination. Let us discuss both in detail.
We know that a permutation is the arrangement of a set of data in some specific order. If we have total number of n datasets and we have to choose r objects from the dataset then the basic permutation formula is given as:
${}^{n}{{P}_{r}}=\dfrac{n!}{\left( n-r \right)!}$
Where, n is the total number of objects and r is the number of choices.
So ${}^{n}{{P}_{r}}$ means that we have to choose r objects from the n number of objects. Hence ${}^{n}{{P}_{r}}$ is the representation of the permutation of objects in math.

Note: Students may confuse between permutation and combination. Combination is the way to choose data from a group of data without any order. If we have to choose r objects from the given n number of objects then the basic combination formula is given as
\[{}^{n}{{C}_{r}}=\dfrac{n!}{r!\left( n-r \right)!}\]
The difference between permutation and combination is that in permutation order of objects is important whereas in combination the sequence or order of selection is not considered.