How many positive integers less than 10,000 are such that the product of their digits is 210?	Choose the correct choice from the following answers:
A) 24
B) 30
C) 48
D) 54
E) 72
210 = 2x5x3x7 = 5x6x7x1 = 5x6x7   Those are the only sets of digits we can use to for the numbers (any other combination of factors will have two digit factors).   Numbers using 2,5,3,7 = 4!   Numbers using 5,6,7,1 = 4!   Numbers using 5,6,7 (3-digit numbers) = 3!   Answer = 24+24+6= 
<gadget id="calculator">24+24+6</gadget>
<output>54</output>
54   Answer is (54)
<result>D</result>
How many positive integers less than 10,000 are such that the product of their digits is 210?