how many six digit number can be formed using the digits 1 to 6, without repetition, such that the number is divisble by the digit at unit's place

• Total possible nos without condition of divisibility = 6! = 720
  
  only some nos with last digit 4 may not be divisible
  which are ending with 14,34,54
  no of such nos are 3*4*3*2 = 72
  
  so six digit number can be formed using the digits 1 to 6, without repetition, such that the number is divisble by the digit at unit's place = 720-72= 648
• 12 years agoHelpfull: Yes(73) No(16)
• Ans. 648
  
  As each number will contain all the six digits and the sum of digits is
  = 1+2+3+4+5+6 = 21 which is divisible by 3. So each number is divisible by 3. The numbers ending with digit 1 will be divisible 1. The numbers ending with digit 2 will be divisible 2. The numbers ending with digit 3 are divisible 3. The numbers ending with digit 5 will be divisible 5. The numbers ending with digit 6 will be divisible 6. Except the numbers ending with last two digits as 14, 34 and 54 all other numbers ending with 4 are divisible by 4.
  
  The no. of numbers ending with last two digits 14,34 and 54 are
  = 3*4*3*2 = 72. (As for a number to be divisible by 4 last two digits must be divisible by 4)
  so six digit number that can be formed using the digits 1 to 6, without repetition, such that the number is divisble by the digit at unit's place
  = 720-72= 648
• 12 years agoHelpfull: Yes(53) No(5)
• If units digit has 1 then possible numbers = 120(5!)---------->1
  _ _ _ _ _ 1 (remaining 5 digits can be filled in 5! ways
  if units digit has 2 then possible numbers = 120-------------->2
  
  if units digit has 3 then possible numbers = 120-------------->3
  as the sum of all digits is 21 the number is divisible by 3
  if units digit has 4 then possible numbers = 48 (4!*2)
  as the last two digits must 24,64 remaining 4 digits can be arranged in 4!*2
  if units digit has 5 then possible numbers = 120
  if units digit has 6 then possible numbers = 120
  total 120+120+120+48+120+120=648
• 10 years agoHelpfull: Yes(46) No(2)
• 
  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
  
• 9 years agoHelpfull: Yes(31) No(0)
• I have gone with the cases putting 1 2 3 4 5 6 as unit digits
  and got the answer as 648(120+120+120+48+120+120)
• 12 years agoHelpfull: Yes(25) No(1)
• thanks arjun bhai....great thinking power
• 10 years agoHelpfull: Yes(14) No(0)
• How you are calculating for divisible by 4.
  I am not getting 3*4*3*2 = 72.from where 3 *4*3*2 is coming.
• 11 years agoHelpfull: Yes(10) No(2)
• 6!-4!*3C1=720-72=648
• 10 years agoHelpfull: Yes(7) No(1)
• ans:2468
  1 as units place=720
  2 as units place=360
  3 as units place=720
  4 as units place=168
  5 as units place=120
  6 as units place=360
  total six digit numbers=720+360+720+168+120+360=2468
• 12 years agoHelpfull: Yes(6) No(66)
• oops i missed something...
  If digit place has 1 then possible numbers = 120(5!)
  if 2 then possible numbers = 120
  if 3 then possible numbers =120
  if 4 then possible numbers = 48 (4!*2)
  if 5 then possible numbers = 120
  if 6 then possible numbers = 120
  so total no=648 now it's right!
• 10 years agoHelpfull: Yes(6) No(1)
• I THINK 648 NUMBERS ARE POSSIBLE.....
• 12 years agoHelpfull: Yes(5) No(17)
• total possible no =6! ie 720
  720/6=120 will b divisible each for 1,2,3,5,6
  for 4 divisible its 2/5*120=48( as 14,24,34,44,54 only out of these only 2 numbers are divisible by 4)
  so total number =120+120+120+120+120+48=648
• 9 years agoHelpfull: Yes(4) No(0)
• 3*4*3*2*1 actually means 3*4!
  3 for 14,34,54 which are not divisible by 4.
  4! are the ways. So Ans is 720-3*4!=648
  
• 10 years agoHelpfull: Yes(3) No(0)
• If digit place has 1 then possible numbers = 120(5!)
  if 2 then possible numbers = 120
  if 3 then possible numbers =120
  if 4 then possible numbers = 48 (4!*2)
  if 5 then possible numbers = 120
  if 6 then possible numbers = 20
  so total no=648
  
• 10 years agoHelpfull: Yes(2) No(1)
• when unit place is 1 then 5*4*3*2*1=120
  when unit place is 2 then 5*4*3*2*1=120
  """""""""""""""""' 3 then 120
  """""""""""""""""" 4 then 24
  """""""""""""""""" 5 then 120
  """""""""""""""""" 6 then 120
  total is 5*120+24=624
• 9 years agoHelpfull: Yes(2) No(1)
• when unit place is 1 then 5*4*3*2*1=120
  when unit place is 2 then 5*4*3*2*1=120
  """""""""""""""""' 3 then 120
  """""""""""""""""" 4 then 24*2 bcuz 24 and 64 is divisible by 4
  """""""""""""""""" 5 then 120
  """""""""""""""""" 6 then 120
  total is 5*120+24=648
• 9 years agoHelpfull: Yes(2) No(0)
• Given number 1,2,3,4,5,6
  when unit digit 1 then number ways=5*4*3*2*1=120
  number way 1,2,3,5,6=120*5=600
  if unit digit 4 then tens place 2,6=4*3*2=24*2=48
  total number of ways=600+48=648
• 8 years agoHelpfull: Yes(2) No(0)
• it should be 528 because the number that ends with 1,2,3,5 are divisible with 1,2,3,5 respectively but the numbers that ends with 4 and 6 has to have second last digit be 2, so with this we have 48 more numbers which gives total of 528...
• 10 years agoHelpfull: Yes(1) No(3)
• u all guys are including 6
  bt ony 36 is divisible by 6
  wat abt 16,26,46,56?????
• 10 years agoHelpfull: Yes(1) No(1)
• digits are divisible by One are=1*5*4*3*2*1=120 (1, , , , ,(2 to 6) )
  digits are divisible by Two are=1*4*3*2*1*2=48 (2, , , , ,(4 or 6) )
  digits are divisible by Three are=1*5*4*3*2*1=120 (3, , , , ,(1 to 6 expect 3) )
  digits are divisible by four are=1*4*3*2*2=48 (4, , , ,(last two digit may be 12 or 16 or 32 or 36 or 52 or 56) )
  digits are divisible by Five are=0, because unit digit is 5 and in last should be 5 or 0, we can't repeat
  digits are divisible by Six are= divisible by 2 or 3 = 48+120=168
  120+48+120+48+0+168=528
• 8 years agoHelpfull: Yes(1) No(5)
• if the question was as like - "six digit no. can be formed using the digit 0 to 5,without repetition.......... .unit's place" ...then what will be answer a.420 b.426 3.432 d.none ???
• 9 years agoHelpfull: Yes(0) No(0)
• I have gone with the cases putting 1 2 3 4 5 6 as unit digits
  and got the answer as 648(120+120+120+48+120+120)
  Read more at http://www.m4maths.com/frequently-asked-placement-questions.php?SOURCE=elitmus&TOPIC=Numerical%20Ability&SUB_TOPIC=Permutation%20and%20Combination#vFws7SICk58fhqWe.99
• 9 years agoHelpfull: Yes(0) No(0)