Assertion :The number of positive integral solutions of $a b c = 30$ is 27. Reason: Number of ways in which three prizes can be distributed among three persons is $3^{3}$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
We have, $30 = 2 \times 3 \times 5$ . So, $2$ can be assigned to either $a$ or $b$ or $c$ , i.e., $2$ can be assigned in $3$ ways. Similarly, each of $3$ and $5$ can
be assigned in $3$ ways. Thus, the number of solutions is $3 \times 3 \times 3 = 27$ .

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