The number of ways in which 16 identical things can be distributed among 4 persons if each person gets at least 3 things, is

Required number = coefficient of x¹⁶ in (x³ + x⁴ + … + x⁷)⁴

                             = coefficient of x¹⁶ in x¹² (1 + x + … + x⁴)

                           $\begin{array}{c}=\text{ coefficient of }{\mathrm{x}}^4\text{ in }{\left(\frac{1-{\mathrm{x}}^5}{1-\mathrm{x}}\right)}^4\\ =\text{ coefficient of }{\mathrm{x}}^4\text{ in }\left[{\left(1-{\mathrm{x}}^5\right)}^4(1-\mathrm{x}{)}^{-4}\right]\\ =\text{ coefficient of }{\mathrm{x}}^4\text{ in }\left[\left(1-4{\mathrm{x}}^5+6{\mathrm{x}}^{10}-\dots \right)(1-\mathrm{x}{)}^{-4}\right]\\ =\text{ coefficient of }{\mathrm{x}}^4\text{ in }(1-\mathrm{x}{)}^{-4}\\ {=}^7{\mathrm{C}}_4=\frac{4\cdot 5\cdot 6\cdot 7}{4!}=35\end{array}$