How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.

• 720-72=648....100% SURE
• 11 years agoHelpfull: Yes(29) No(3)
• when units digit is 1.... no of ways are 5! (since every no is divisible by 1).
  when unit digit is 2.... no of ways is 5!(since inorder to divisible by 2 , units digit must be even number, in this case only 2.)
  when unit digit is 3.... sum must be divisible by 3..... so 6,5,4,2,1 can be placed in any place,since it will be divisible by 3, so 5! ways.
  when 4 in units place, 64,24 must be in unit and tens place in such a way to get divisible by 4....so no of ways are 3*4! ways.
  when 5 in units place, no of ways 5! ways.
  when 6 also ,it is 5! ways.
  
  So totally answer is 5!+5!+5!+(2*4!)+5!+5!=648 ways........
  
  
  @anchuri ur process ws crrct d only mstk u hv dn is dt u repeat 44 ...nd fr ds d ansr ws chngd ... gd 1 bro keep it up
• 11 years agoHelpfull: Yes(18) No(2)
• Sorry i have done one mistake in below submitted one....
  when units digit is 1.... no of ways are 5! (since every no is divisible by 1).
  when unit digit is 2.... no of ways is 5!(since inorder to divisible by 2 , units digit must be even number, in this case only 2.)
  when unit digit is 3.... sum must be divisible by 3..... so 6,5,4,2,1 can be placed in any place,since it will be divisible by 3, so 5! ways.
  when 4 in units place, 64,24 must be in unit and tens place in such a way to get divisible by 4....so no of ways are 2*4! ways.
  when 5 in units place, no of ways 5! ways.
  when 6 also ,it is 5! ways.
  
  So totally answer is 5!+5!+5!+(2*4!)+5!+5!=648 ways........
• 11 years agoHelpfull: Yes(5) No(1)
• actually numbers are not be repeated.hence when unit digit is 4 ,the no of possible 6 digit no will be 48,hence we get 600+48=648
• 11 years agoHelpfull: Yes(4) No(2)
• when unit digit will be 1 or 2 or 3 or 5 or 6 then all the numbers formed will be divisible by these numbers respectively.
  by taking one of these numbers at unit place,other place can be filled by 5!
  when unit digit will be 4, 10th place can be filled by 6 or 2 i.e 2 ways..other places can be filled by 4!
  so, total numbers formed = 5*5!+2*4!=648
  
• 11 years agoHelpfull: Yes(4) No(1)
• optios-
  a)360
  b)648
  c)660
  d)720
• 11 years agoHelpfull: Yes(2) No(1)
• when unit digit = 1 ,then no. of way is 5!(last digit 5 is fixed and remaining initial 5 digits are can be rearrange b/w 5 places by 5! way).
  so no. of way= 5!.
  when unit digit =2, then no. way= 5!also
  when unit digit = 3, (d sum of total no. is divisible by 3).and no. of way =5!
  when unit digit =4,(and last two digits are 64 or 24 both are divisible by 4), no. of way =2*4!.
  when unit digit =5, no of way= 5!.
  when unit digit =6, no of way =5!(2*3=6,and the sequence is divisible by 2&3 both so also divisible by 6)
  total no of way=(5!)+(5!)+(5!)+(2*4!)+(5!)+(5!)= 648.
• 11 years agoHelpfull: Yes(2) No(1)
• when units digit is 1.... no of ways are 5! (since every no is divisible by 1).
  when unit digit is 2.... no of ways is 5!(since inorder to divisible by 2 , units digit must be even number, in this case only 2.)
  when unit digit is 3.... sum must be divisible by 3..... so 6,5,4,2,1 can be placed in any place,since it will be divisible by 3, so 5! ways.
  when 4 in units place, 64,24 must be in unit and tens place in such a way to get divisible by 4....so no of ways are 8*4!(as last two digits will be 12,16,24,32,36,52,56,64) ways.
  when 5 in units place, no of ways 5! ways.
  when 6 also ,it is 5! ways.
  
  So totally answer is 5!+5!+5!+(8*4!)+5!+5=768
• 11 years agoHelpfull: Yes(2) No(3)
• anchuri why 44 is repition allowed.......
• 11 years agoHelpfull: Yes(2) No(0)
• when units digit is 1.... no of ways are 5! (since every no is divisible by 1).
  when unit digit is 2.... no of ways is 5!(since inorder to divisible by 2 , units digit must be even number, in this case only 2.)
  when unit digit is 3.... sum must be divisible by 3..... so 6,5,4,2,1 can be placed in any place,since it will be divisible by 3, so 5! ways.
  when 4 in units place, 64,24,44 must be in unit and tens place in such a way to get divisible by 4....so no of ways are 3*4! ways.
  when 5 in units place, no of ways 5! ways.
  when 6 also ,it is 5! ways.
  
  So totally answer is 5!+5!+5!+(3*4!)+5!+5!=672 ways........
• 11 years agoHelpfull: Yes(1) No(10)
• we can form 6! ways
  
  so 6!=720
• 11 years agoHelpfull: Yes(1) No(10)
• You have 6 choices for the units digit, leaving 5 choices for the tens digit, leaving 4 choices for the hundreds digit, and so on. In all, 6*5*4*3*2*1 different numbers.
• 11 years agoHelpfull: Yes(1) No(4)
• kahin se copy kiya h kya......every tyme @achuri u hv written same same....why dont u explain how...if 6 digit no. can be formed then how come 5!
• 11 years agoHelpfull: Yes(1) No(1)
• hi for the no.to be divisible by 4 the condition is sum of last two digits is divisible by 4 then how 64 i.e..6+4=10 and 24 i.e..2+4=6 are not divisible by 4 can be considered please give the correct solution
• 10 years agoHelpfull: Yes(0) No(1)