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Question

The number of natural numbers which lie between 108 and 109 which have products of their digits as 6 is___.

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Solution

108<n<109

n is a 9 digit number

Product of 6 is possible in the following cases

Exactly one digit is 6 and the remaining digits are 1

Number of possible numbers= 9

One digit is 2 and the other is 3, remaining are 1 = 9P2 = 72

Total possible numbers = 72+9 = 81


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