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

We know that

$7-x>0 ; x-3 \geq 0$ and $7-x \geq x-3$

$\Rightarrow x<7 ; x \geq 3$ and $2 x \leq 10$

$\Rightarrow x<7 ; x \geq 3$ and $x \leq 5$

So, $x=\{3,4,5\}$

Range of $f$

$=\left\{{ }^{(7-3)} P_{(3-3)},{ }^{(7-4)} P_{(4-5)},{ }^{(7-5)} P(5-3)\right\}$

$=\left\{4 P_{0}, 3 P_{1}, 2 P_{2}\right\}$

$=\{1,3,2\}$

$=\{1,2,3\}$

So, the answer is (d).