find the number of 6 digit numbers that can be formed using digits 1,2,3,4,5,6 once such that the 6digit number is divisible by its unit digit.  Choose the correct choice
A) 646 B) 648 C) 650 D) 652 E) 654
There are 6 numbers which can be placed in units digits.   case 1: When the unit digit is 1,2,3,5,6 whatever the other numbers are the 6 digit number will be surely divisible by the unit digit.   Hence the 5 numbers in the units place can be placed in 5 ways and the remaining 5 numbers can be arranged in 5! ways.   5*5!=600 ways   Case 2: If the unit digit is 4, then the tens digit should be 2 or 6, hence 24 or 64 can be arranged in the last two places in 2 ways and the remaining 4 numbers can be arranged in 4 places in 4!ways.   2*4!=48 ways   Total no.of.ways= 600+48= 
<gadget id="calculator">600+48</gadget>
<output>648</output>
648 ways.   ANSWER:648
<result>B</result>
find the number of 6 digit numbers that can be formed using digits 1,2,3,4,5,6 once such that the 6digit number is divisible by its unit digit.