• # question_answer The number of positive integral solutions of $a\,b\,c=30$is [UPSEAT 2001] A) 30 B) 27 C) 8 D) None of these

Correct Answer: B

Solution :

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 no. of solutions are 3 × 3 × 3 = 27.

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