\ Total number of elements in the range of the function $f\left(x\right){=}^{7-x}{P}_{x-3}\text{ is }$

$\begin{array}{l}P\left(7-x,x-3\right)\text{ is defined if }7-x\ge 0\text{\hspace{0.17em} and }x-3\ge 0\text{\hspace{0.17em} and }7-x\ge x-3\\ \text{Hence, }x=3,4,5\\ \text{The range is }f\left(3\right),f\left(4\right),f\left(5\right)=\left\{1,2,3\right\}\end{array}$