Question

What does $r$ mean in ${}^{n}P_r$?

Answer 1

Meaning of $\mathbf{r}$ in ${}^{\mathbf{n}}\mathit{P}_{\mathbf{r}}$:

• The permutation is the arrangement of elements in a definite order.
• ${}^{n}P_r$ denotes permutation.
• The variable $n$in the term ${}^{n}P_r$ is the number of elements in the given set.
• The variable $r$ in the term ${}^{n}P_r$ denotes the number of elements selected from the total number of objects.
• The formula of ${}^{n}P_r$ is $\frac{\mathbf{n}\mathbf{!}}{\left(n-r\right)\mathbf{!}}$.

For example: Find the number of 3 letter words that can be formed by rearranging the letters of the word MATH?

Here, $n=4,r=3$,

So,total arrangements $=\frac{\mathbf{n}\mathbf{!}}{\mathbf{(}\mathbf{n}\mathbf{-}\mathbf{r}\mathbf{)}\mathbf{!}}=\frac{4!}{(4-3)!}=4!=24$

Hence, the meaning of $\mathbf{r}$ in ${}^{\mathbf{n}}\mathbf{P}_{\mathbf{r}}$ is explained.