Explanation

(a)
Sum of the coefficients in the expansion of
${(x - 2y + 3\mathcal{z)}}^{n}\ is\ {(1 - 2 + 3)}^{n} = 2^{n}$
$(Put\ x = y = \mathcal{z} = 1)$
${\therefore\ 2}^{n} = 128$
$\Rightarrow \ n = 7$
Therefore, the greatest coefficient in the expansion of ${(1 + x)}^{7}$ is $\ ^{7}C_{3}$ or $\ ^{7}C_{4}$ because both are equal to 35