Question

What is the value of ${}^{4}P_4$?

Answer 1

Evaluating ${}^{4}P_4$:

We know that ${}^{n}P_r=\frac{n!}{\left(n-r\right)!}$.

Here, $n=4,r=4$. Thus

$$\begin{gathered} {}^{4}P_4 \\ =\frac{4!}{\left(4-4\right)!}\left[\because 0!=1\right] \\ =4! \\ =4\times 3\times 2\times 1 \\ =24\left[\because 4!=24\right] \end{gathered}$$

Therefore, ${}^{4}P_4=24$.