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  4. Four boys picked up 30 mangoes. The number of ways in which they can divide them if all mangoes be identical, is

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Q. Four boys picked up $30$ mangoes. The number of ways in which they can divide them if all mangoes be identical, is

Permutations and Combinations

Solution:

Clearly, $30$ mangoes can be distributed among $4$ boys such that each boy can receive any number of mangoes.
Hence, total number of ways $={ }^{30+4-1} C_{4-1}={ }^{33} C_{3}$
$=\frac{33.32 .31}{1.2 .3}=5456$