Explanation

(b)
Required number of ways
=coefficient of $x^{16}$in $\left( x^{3} + x^{4} + x^{5} + .\ldots.. + x^{16} \right)^{4}$
=coefficient of $x^{16}$in $x^{12}\left( 1 + x + x^{2} + .\ldots... + x^{12} \right)^{4}$
=coefficient of $x^{4}$ in $\left( 1 - x^{13} \right)^{4}(1 - x)^{- 4}$
=coefficient of $x^{4}$ in $(1 - 13x^{5} + .\ldots)$
$\times \left\lbrack 1 + 4x + .\ldots.. + \frac{(r + 1)(r + 2)(r + 3)}{3!}x^{r} \right\rbrack$
$= \frac{(4 + 1)(4 + 2)(4 + 3)}{3!} = 35$