$\begin{array}{1 1} 75 \\ 150 \\ 210 \\ 243 \end{array}$

Total no. of balls $=5$

No. of persons $=3$

Each person should get atleast one ball.

$\therefore$ The selection of balls can be done by

$(1,1,3)$ or $ (2,2,1)$

$i.e., \:(^5C_1\times.^4C_1\times^3C_3) \:\:or\:\:(^5C_2\times^3C_2\times^1C_1)$

$=(5\times 4\times 1)\:\:or\:\:(10\times 3\times 1)$

$=(20)\:\:or\:\:(30)\:\:ways.$

After selection it should be distributed between three different persons.

$(1,1,3)$ selection is distributed in $\large\frac{3!}{2!}$$=3$ $ways\:\:and$

$(2,2,1)$ selection is distributed in $\large\frac{3!}{2!}$$=3$ $ways.$

$\therefore$ The required no. of ways $=(20\times 3)+(30\times 3)$

$=60+90=150$

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