How many six digits no can be formed using the digits 1 to 6,without repetation such that the number is divisible by the digit at its unit place??
(a)402
(b)528
(c)648
(d)720

• 648
  when unit digit is 1 =5!
  _ _ _ _ _ 2 = 5!
  _ _ _ _ _ 3 = 5!
  when last two digits are 2 4 and 64 = 4! * 2
  _ _ _ _ _ 5 = 5!
  _ _ _ _ _ 6 = 5!
  
  total 5*5!+2*4! =648
• 11 years agoHelpfull: Yes(12) No(3)
• 528
  _ _ _ _ _ 2 = 5!
  _ _ _ _ _ 3 = 5
  _ _ _ _ 2 4 and 64 = 4! * 2
  _ _ _ _ _ 5 = 5!
  _ _ _ _ _ 6 = 5!
  
• 11 years agoHelpfull: Yes(4) No(4)
• when unit digit is 1=5!
  -------------------2=5!
  -------------------3=5!
  when last two digit's are 24,64 =2*3!
  -------------------5=5!
  -------------------6=5!
  total 5*5!+2*4! =648
  
• 11 years agoHelpfull: Yes(2) No(0)
• 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 = 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 = 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 = 648
• 7 years agoHelpfull: Yes(0) No(0)
• in all the soln u guys have taken 24 and 64 for 4 but why haven't u considered 12,16,16,56,52,32. these are also divisible by 4 .
  so the answer will be
  _ _ _ _ _ 1 =5!
  _ _ _ _ _ 2 =5!
  _ _ _ _ _ 3 =5!
  _ _ _ _ _ 4=4!
  _ _ _ _ _ 5=5!
  4!+5!*5=624
• 7 years agoHelpfull: Yes(0) No(1)