How many 4 digit numbers can be formed using the digits 1,2,3,4,5 (but with repetition) that are divisible by 4?

• Digits that can be used = 1, 2, 3, 4 and 5
  For a number to divisible by 4, the last two digits have to be divisible by 4
  So, the units digit cannot be 1, 3 or 5
  If the units digit is 2, only 12, 32 adn 52 are acceptable as the last two digits
  If the units digit is 4, only 24 and 44 are acceptable as the last two digits.
  So, total 5 cases for the last two digits.
  Now, the first 2 digits of the 4 digit number can be filled in 5^2 ways as each place can be filled by 1, 2, 3, 4 or 5.
  So, desired answer = 5^n-1 where n is no of digits
  ans is 5^3
• 12 years agoHelpfull: Yes(38) No(27)
• Possibilities of last 2 digits which are divisible by four are 12,24,32,44,52 only.And remaining first two places have 5 possibilities(each one because repetition is allowed) so total possibilities are
  5*5*5=125
• 9 years agoHelpfull: Yes(21) No(2)
• place can be fill as->5*5*5*3=375
• 9 years agoHelpfull: Yes(7) No(6)
• 1, 2, 3, 4 and 5 must be used.
  for divisibility by 4, the last two digits have to be divisible by 4 i.e (2 or 4)
  
  If the units digit is 2, only 12, 32 and 52 are possible--> 3 cases
  If the units digit is 4, only 24 and 44 are acceptable as the last two digits -->2 cases
  total 5 cases for last 2 digits
  
  Now, the first 2 digits of the 4 digit number can be filled in 5 x 5 ways as each place can be filled by 5 digits with repetition so max is 5x5=25 cases for each of 5 cases of last 2 digits
  So, desired answer = 5 x 5 x 5= 125 (answer)
• 9 years agoHelpfull: Yes(6) No(0)
• For a number to divisible by 4,the last two digits have to be divisible by 4
  So, the units digit can only be 2 and 4
  Possibilities of last 2 digits which are divisible by four are 12,24,32,44,52 only
  so total cases four four digit no. is....
  ans- 5*5*5*2
  
• 9 years agoHelpfull: Yes(5) No(7)
• according to divisibility rule of 4 last two digits must be 53 or 35
  so there remaining two numbers can be set as 20+2=22
  22 is ans
• 9 years agoHelpfull: Yes(4) No(11)
• digits at 1st 2 places can be arranged into 5*5 =25 ways and digits at unit and tenth place can have only 5 combinations i.e (1,2),(2,4),(3,2),(4,4),(5,2) so answer will be 25*5 or say 5*5*5=125
• 8 years agoHelpfull: Yes(4) No(0)
• 5 places. first three can have 5 possibilities each and the last can have 3 only ,that are 24,32,54. thus 5*5*5*3=375
• 10 years agoHelpfull: Yes(3) No(11)
• last digits can be 12,24,32,42,54
  5*5*5
  =125
• 8 years agoHelpfull: Yes(3) No(1)
• 125
  1st two digits can be arranged in 5*5 ways.the next two digits can have only 5 commbinations.
  thus the answer is 5*5*5=125
• 8 years agoHelpfull: Yes(2) No(0)
• 5!*4!*3!*2!=34560
• 8 years agoHelpfull: Yes(1) No(2)
• first digit can be filled by 5 ways ,second can be 5 ways and third also can be filled by 5 ways and fourth can be only ways because the number should be divisible by 4 that why the answer will be 5*5*5*2 = 250
• 8 years agoHelpfull: Yes(1) No(0)
• answer wud be 375
  as for any no to be divisible by 4 its last digit should be also divisible by 4..
  n such cases is possible with 12, 32, 52
  now we've 3 cases to proceed n in each case there are 5*5*5=125 possible arrangements
  so total pssbl arrngmnts= 125*3=375
• 8 years agoHelpfull: Yes(1) No(0)
• as 12,24,32,44,52 last two digit
  & first two digit for 1--- 11 12 13 14 15 possible*5=25
  & similarly for 2---------21 22 23 24 25 *5=25...
  25*5=125
• 8 years agoHelpfull: Yes(1) No(0)
• last digit will be 2 or 4
  so the number of ways is is 5*5*5*2=250
• 8 years agoHelpfull: Yes(1) No(0)
• fro a number to be divisible by 4, last two digit must be divisible by 4.
  therefore,possible last two digits can be 12,24,32,52.
  hence, the rest two digit can be arranged in 5*5 ways = 25
  4*25=100 ways
  
• 8 years agoHelpfull: Yes(0) No(0)
• the last number of digit number which divisible from 1 2 3 4 5 is 4,2.
  there fore last digit can be filled in 2 ways,then reaming 3 digits can be filled in 5 ways because repetitions allowed.
  5*5*5*2=250
  
• 7 years agoHelpfull: Yes(0) No(0)
• _ _ 32
  _ _ 28
  _ _ 24
  _ _ 52
  there are four possibilities for divisible by 4
  ans. 200 such numbers can be there
• 5 years agoHelpfull: Yes(0) No(0)