How many 6 digit no can be formed by 0,1,2,3,4,5 so that no is divisible by unit place digit

• take 5 at unit place the _ _ _ _ _ 5 thn it is 4*4! and nw take 4 thn it have two cases _ _ _ _ 0 4 and _ _ _ _ 2 4 thn it is 4*3!+3*3! and again for 3 _ _ _ _ _ 3 thn it is 4*4! and nw for 2 it is _ _ _ _ _ 2 so 4*4! and similarly for 1 4*4! so we add oll (4*4!)+(4*3!+3*3!)+(4*4!)+(4*4!)+(4*4!)= 96+(24+18)+96+96+96= 426
• 10 years agoHelpfull: Yes(49) No(8)
• fix unit digit :-
  for 1 : 96 ways
  for 2: 96 ways
  for 3: 96 ways
  for 4:case 1: when last two digit 04 then 24 ways
  case 2: when last two digit 24 then 18 ways
  for 5: 96 ways
  
  so all the possible number can formed = 96*4+(24+18) = 426.
• 9 years agoHelpfull: Yes(11) No(0)
• total=522
  1._ _ _ _ _ 0=5*4*3*2*1=120
  2._ _ _ _ _ 1=4*4*3*2*1=96
  3._ _ _ _ _ 2=4*4*3*2*1=96
  4._ _ _ _ _ 3=4*4*3*2*1=96
  5._ _ _ _ _ 4=3*3*2*1=18
  6._ _ _ _ _ 5=96
  total=522
• 10 years agoHelpfull: Yes(9) No(14)
• Ans is 546
  0=120
  1=4*4!
  2=4*4!
  3=4*4!
  4=4!+3*3!
  5=4*4!
• 10 years agoHelpfull: Yes(3) No(1)
• 408
  fix last digit-
  '1'---- 96 ways
  '2'---- 96 ways
  '3'---- 96 ways
  '4'---- 24 ways
  '5'---- 96 ways
• 10 years agoHelpfull: Yes(2) No(1)
• to be divisible by zero the number should end in zero.. for that there are 120 possibilities
• 10 years agoHelpfull: Yes(2) No(2)
• Case 1(When last digit is 5):
  
  _ _ _ _ _ 5 and 1st digit should not be 0 so fill 1st place 4type and 2nd place has also 4types and 3rd place as 3types 4thplace has 2types so total will be=4*(4*3*2)=4*4!
  
  Case 2(Last digit is 4):
  in this we have two sub case (last two digits should be either 04 or 24)
  Sub case 1(last two digits are 04):
  _ _ _ _ 04 so 1st place can be filled in 4types,2nd place can be filled in 3types,3rd place can be filled in 2types,4th place can be filled one type so total ways=4!
  Sub case 2(last two digits are 24)
  _ _ _ _24 so first place can be filled in 3 ways,2nd place can be filled in 3types,3rd place can be filled in 2types,4th place can be filled one type so total ways=3*3!
  
  Case 3(Last digit is 3):
  as sum of all digit is 15 so any no. will be divisible by 3
  _ _ _ _ _3 and 1st digit should not be 0 so fill 1st place 4type and 2nd place has also 4types and 3rd place as 3types 4thplace has 2types so total will be=4*(4*3*2)=4*4!
  
  Case 4(Last digit is 2):
  as all no. end with 2 will be divisible by 2
  _ _ _ _ _2 and 1st digit should not be 0 so fill 1st place 4type and 2nd place has also 4types and 3rd place as 3types 4thplace has 2types so total will be=4*(4*3*2)=4*4!
  
  Case 5(Last digit is 1):
  as all no. end with 1 will be divisible by 1
  _ _ _ _ _1 and 1st digit should not be 0 so fill 1st place 4type and 2nd place has also 4types and 3rd place as 3types 4thplace has 2types so total will be=4*(4*3*2)=4*4!
  
  
  
  
• 9 years agoHelpfull: Yes(2) No(0)
• Repetation alowed or not
  
• 10 years agoHelpfull: Yes(1) No(1)
• (432)
  5 >> 96
  4 >> 4*3*2*1*2=48
  3 >> 96
  2 >> 96
  1 >> 96
  0 >> 0
• 10 years agoHelpfull: Yes(1) No(0)
• For 0 at unit place:0 cases
  For 1 at unit place:4*4*3*2*1*1 cases=96 cases
  For 2 at unit place:4*4*3*2*1*1 cases=96 cases
  For 3 at unit place:4*4*3*2*1*1 cases=96 cases
  For 4 at unit place:
  CASE1:for 04 as last two digits=4*3*2*1*1*1 cases=24 cases
  CASE2:for 24 as last two digits=3*3*2*1*1*1 cases=18 cases
  total=42 cases
  For 5 at unit place:4*4*3*2*1*1 cases=96 cases
  Answer=426
• 9 years agoHelpfull: Yes(1) No(0)
• Ans: for 0-5!=120
  1-No one
  2-No one
  3-No one(1+2+3+4+5=15)
  4-3*(3*3!)=54(-,-,-,-,1/3/5,4)
  5-No one
  Ans=120+54=174
• 10 years agoHelpfull: Yes(0) No(11)
• Thnx for this questions
  
  
• 10 years agoHelpfull: Yes(0) No(0)
• 0,1,2,3,4,5
  TOTAL NO 6
  SO 6!=720
  But in this 720 ways ther exists a numbers starting by 0 012345
  012564
  like so ways -----
  5!=120
  all the numbers which started by 0 are'nt 6 digit
  so 720-120
  -----------------answer---600 6 digit numbers
• 10 years agoHelpfull: Yes(0) No(1)
• how 4*3!+3*3! become
• 10 years agoHelpfull: Yes(0) No(1)
• (420)
  5 >> 96
  4 >> 3*3*2*2*1=36
  3 >> 96
  2 >> 96
  1 >> 96
  so total numbers are 420
• 10 years agoHelpfull: Yes(0) No(1)
• _ _ _ _ _ _ 0 ----> 120 ways
  _ _ _ _ _ _ 1 -----> 96 ways
  _ _ _ _ _ _ 2 -----> 96 ways
  _ _ _ _ _ _ 3 -----> 96 ways
  _ _ _ _ _ _ 4 -----> 48 ways (last two digits must be 04 or 24)
  _ _ _ _ _ _ 5 -----> 96 ways
  
  total ways = 552 ways
  
• 9 years agoHelpfull: Yes(0) No(0)