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Q.
Number of positive integral solutions of $x_1 \cdot x_2. \cdot x_3=30$ is
Permutations and Combinations
Solution:
We have $30 = 2.3.5$. We can assign in $2$ to $x_{1}$ or $x_{2} $ or $x_{3}$ That is $2$ can be assigned in $3$ ways. Similarly each of $3$ and $5$ can be assigned in $3$ Ways. Thus the numbers of solutions $= 3 \times 3\times 3$
$ = 27$.