nPr Formula

About nPr Formula

In the nPr formula, the letter "P" stands for "permutation," which signifies "arrangement."
The nPr formula calculates the number of possible combinations for picking and arranging r items from a set of n items. Sometimes the layout is crucial.
P (n, r) (or) n P r (or) n P r can be written as nPr. It's used to figure out how many distinct methods there are to choose and arrange r different things from n different things. The permutations formula is also known as the nPr formula (as we call a way of choosing and arranging things to be a permutation). Factorials are used in this formula. The nPr formula is shown below.

The nPr formula is,

n! / (n - r)!=P (n, r) (or) ⁿP_r (or) _n P_r

where

Consider n various things and the assumption that r separate objects should be chosen and ordered from them. Let's look into a few other options.

Because there are n things in total, there are n ways to choose the first one.

Because the first thing has already been picked, the number of options for selecting the second object is limited (n - 1).

Similarly, there are numerous options for selecting the third object (n - 2).

There are only (n - r + 1) objects remaining to choose from when choosing the rth object, hence it

can be picked in (n - r + 1) ways.
The number of ways (nPr) of picking and arranging r different objects from n different objects is, according to the fundamental counting principle.
n (n - 1) (n - 2) ... (n - r + 1) = n P r
We use factorial notations to make things easier. Multiplying and dividing (n - r) by the above expression... 3 • 2 • 1
n P r = [n (n - 1) (n - 2) ...(n - r + 1) (n - r) ... 3 • 2 • 1] / [(n - r) ... 3 • 2 • 1] = n! / (n - r)!
Thus, the nPr formula is derived.

Get a List of Maths Formulas on one page