Explanation

(c)
Given function is $f(n) = 8 -^{n}P_{n - 4},\ 4 \leq n \leq 6$. It is defined, if
1. $8 - n > 0 \Rightarrow n < 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
2. $n - 4 \geq 0 \Rightarrow n \geq 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
3. $n - 4 \leq 8 - n \Rightarrow n \leq 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(iii)$
From Eqs. (i), (ii) and (iii), we get $n = 4,\ 5,\ 6$
Hence, range of $f(n) = \left\{ \ ^{4}P_{0},\ \ ^{3}P_{1},\ \ ^{2}P_{2} \right\} = \{ 1,\ 3,\ 2\}$