Assertion :The number of positive integral solutions of abc=30 is 27. Reason: Number of ways in which three prizes can be distributed among three persons is 33
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
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=2×3×5. 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 3×3×3=27.