Solution
assuming all oranges are identical
Let children $\mathrm{C}_{1}, \mathrm{C}_{2}, \mathrm{C}_{3}, \mathrm{C}_{4}$ get number of oranges $\mathrm{x}_{1}, \mathrm{x}_{2}, \mathrm{x}_{3}, \mathrm{x}_{4}$
$\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\mathrm{x}_{4}=16$ where $\mathrm{x}_{1}, \mathrm{x}_{2}, \mathrm{x}_{3}, \mathrm{x}_{4} \geq 1$
let $\mathrm{x}_{\mathrm{i}}=\mathrm{x}_{\mathrm{i}}^{\prime}+1 ; \mathrm{x}_{1}^{\prime}+\mathrm{x}_{2}^{\prime}+\mathrm{x}_{3}^{\prime}+\mathrm{x}_{4}^{\prime}=12$
Number of non-negative integral solutions ${ }^{n+p-1} C_{p-1}={ }^{12+4-1} C_{4-1}$
$={ }^{15} \mathrm{C}_{3}=455$ Answer(4)
.
