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Previous Year Question (PYQs)
How many positive numbers less than 10,000 are such that the product of their digits is 210?
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210=1*2*3*5*7=1*6*5*7.(Only 2*3 makes the single digit 6).
So, four digit numbers with combinations of the digits {1,6,5,7} and {2,3,5,7} and three digit numbers with combinations of digits {6,5,7} will have the product of their digits equal to 210.
{1,6,5,7} # of combinations 4!=24
{2,3,5,7} # of combinations 4!=24
{6,5,7} # of combinations 3!=6
24+24+6=54.
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