Question:
In how many ways can 5 bananas be distributed among 3 boys, there being no restriction to the number of bananas each boy may get?
Solution:
As there is 5 banana, So suppose it as $B_{1}, B_{2}, B_{3}, B_{4}, B_{5}$ And Let the Boy be $\mathrm{A}_{1}, \mathrm{~A}_{2}, \mathrm{~A}_{3}$
So $B_{1}$ can Be distributed to 3 Boys $\left(A_{1}, A_{2}, A_{3}\right)$ by 3 ways,
Similarly, $B_{2}, B_{3}, B_{4}, B_{5}$ Can be distributed to 3 Boys by $3^{4}$
So total number of ways is $3^{5}$