The range of the function $f (x)={^{7-x}P}_{x - 3}$, is

{1, 2, 3}

Clearly, $f (x)={^{7-x}P}_{x - 3}$ is defined for positive integer values of x satisfying

$7-x >0, x-3≥0$ and $x-3≤7-x$

i.e. $x <7, x≥ 3$ and $x ≤5$

i.e. $x=3,4,5$

∴ Domain (f) = {3, 4, 5}

Hence, range (f) = $\{f (3), f (4), f (5)\} = \{{^4P}_0,{^3P}_1,{^2P}_2\}$

= {1, 2, 3}