Question type: Counting
Case 1: 4 places integer less than 10000
—> 1st 210=1*2*3*5*7
—-> 2nd 210 =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)
{1,6,5,7} # of combinations 4!=24
{2,3,5,7} # of combinations 4!=24
Case 2: 3 digit number= three digit numbers with combinations of digits {6,5,7}
will have the product of their digits equal to 210.
{6,5,7} # of combinations 3!=6
Total=24+24+6= 54
24+24+6=54.
Answer: D.