How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.
Choose the correct answer:
A) 648
B) 720
C) 890
D) 980
E) None of these
Explanation :   Since, there is no repetition, numbers 1 to 6 will always be present in the 6 digit number.   We will go through this step by step.   Divisible by 1 and 1 at the unit place:   _ _ _ _ _ 1   This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.   Divisible by 2 and 2 at the unit place:   _ _ _ _ _ 2   This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.   Divisible by 3 and 3 at the unit place:   _ _ _ _ _ 3   Since, any number will have all the digits from 1 to 6 and the sum  1 + 2 + 3 + 4 + 5 + 6= 
<gadget id="calculator"> 1 + 2 + 3 + 4 + 5 + 6</gadget>
<output>21</output>
21 is divisible by 3   This gives us total of 5 x 4 x 3 x 2 x 1= 120 numbers.   Divisible by 4 and 4 at the unit place:   _ _ _ _ _ 4   Here, there are two cases   _ _ _ _ 2 4   This gives 4 x 3 x 2 x 1 = 24 numbers.   _ _ _ _ 6 4   This gives 4 x 3 x 2 x 1 = 24 numbers.   This gives us total of   24 + 24= 
<gadget id="calculator">  24 + 24</gadget>
<output>48</output>
48 numbers.   Divisible by 5 and 5 at the unit place:   _ _ _ _ _ 5   This gives us total of 5 x 4 x 3 x 2 x 1= 120 numbers.   Divisible by 6 and 6 at the unit place:   _ _ _ _ _ 6   As all 6 digit numbers formed with 1 to 6 digits(without repetition) are divisible by 3 and numbers with 6 at the unit place are even.   This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers.   None of these cases will have numbers overlapping with each other.   So, Total numbers = 120 + 120 + 120 + 48 + 120 + 120= 
<gadget id="calculator">120 + 120 + 120 + 48 + 120 + 120</gadget>
<output>648</output>
648   648nswer : 648
<result>A</result>
How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.