How many positive integers W less than 10,000 are such that the product of their digits is 210?
Pick one.
A) 24  B) 30  C) 48  D) 54  E) 72
210 is the answer when 2, 3, 5 and 7 are multiplied. 210 can also be arrive using 5,6 and 7 and 1, 5, 6 and 7.   So sum of arrangements of 2357, 567 and 1567. This translates to 4! +3! + 4!, this equals to  24 + 6 + 24= 
<gadget id="calculator"> 24 + 6 + 24</gadget>
<output>54</output>
54, 54 is the answer.
<result>D</result>
How many positive integers W less than 10,000 are such that the product of their digits is 210?