Question

Four boys picked up $30$ mangoes. In how many ways can they divide them if all mangoes are identical?

Answer 1

Clearly, $30$ mangoes can be distributed among $4$ boys such that each boy can receive any number of mangoes.
Hence the total number of ways
$={}^{30+4-1}{C}_{4-1}$
$={}^{33}{C}_3$
$=\frac{\mathrm{33.32.31}}{\mathrm{1.2.3}}=5456$