How many positive integers less than 10,000 are such that the product of their digits is 30?
Choose the correct choice from the following answers:  A) 12  B) 24  C) 36  D) 38  E) 50
30 = 1 * 30, 2 * 15, 3* 10, 5 *6   We have the option of using single digits 1,2,3,5 and 6   No : of four digit numbers such that the product is 30   The possible combinations are using digits (1,2,3,5) &amp; (1,1, 5, 6) such that the product 30.   No: of different combinations possible using (1,2,3,5) = 4! = 24   No: of different combinations possible using (5,6,1,1) = 4!/2! = 12 ('1' is repeated twice)   Total 4 digit numbers so that the product is 30 is  24+12= 
<gadget id="calculator"> 24+12</gadget>
<output>36</output>
36   No: of three digit numbers such that the product is 30   The possible combinations are using digits (2,3, 5) &amp; (1,5,6)   No: of different combinations possible using (2,3,5)= 3! = 6   No: of different combinations possible using (1,5,6) = 3! = 6   Total 3 digit numbers so that the product is 30 is  6+6= 
<gadget id="calculator"> 6+6</gadget>
<output>12</output>
12   No: of 2 digit numbers such that the product is 30 is 2 (56 and 65)   Total numbers under 10000 such that the product is 30 is  36+12+2= 
<gadget id="calculator"> 36+12+2</gadget>
<output>50</output>
50   50
<result>E</result>
How many positive integers less than 10,000 are such that the product of their digits is 30?