Explanation

(d)
$\ ^{16}C_{r} = \ ^{16}C_{r + 1}$
$\Rightarrow \ \ \ \ ^{16}C_{16 - r} = \ ^{16}C_{r + 1}\ \ \ \ \ \ \lbrack\because\ \ \ ^{n}C_{r} = \ ^{n}C_{n - r}\rbrack$
$\Rightarrow \ \ 16 - r = r + 1\ \ \ \Rightarrow \ \ 2r = 15$
$\Rightarrow \ \ \ \ \ r = 7.5$
Which is not possible, since $r$ should be an integer