Alok is attending a workshop "How to do more with less" and today's theme is Working with fewer digits . The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as womankind) had only worked with fewer digits.

The problem posed at the end of the workshop is

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

Can you help Alok find the answer?

• 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 12,24,32,44,52 are possible for the last two digits.
  Now, the first 3 digits of the 5 digit number can be filled in 5^3 ways as each place can be filled by 1, 2, 3, 4 or 5.
  So, desired answer = 5^3*5 = 5^4
• 12 years agoHelpfull: Yes(35) No(5)
• for a number to be divisible by 4,we must check that the last two digits should be divisible by 4...
  the combinations of digits formed by 1,2,3,4,5 which are divisible by 4 are
  (1,2),(2,4),(3,2)(4,4),(5,2)
  so it means out these 5 pairs we must select a 1 pair for the number to be divisible by 4...
  so its probability is 5C1=5
  
  now we have selected last two digits ..
  
  now our task is to select the first 3 digits in a number.they can be any digits ie(1,2,3,4,5)..
  because repetition is allowed
  number of possibilities for 1st place =5
  number of possibilities for 2nd place =5
  number of possibilities for 3rd place =5
  so total possibilites at 1st,2nd,3rd place =5^3
  
  
  total probalitiy is=5^3+5C1=5^4
  
  hence our answer is 5^4=625
• 11 years agoHelpfull: Yes(6) No(2)
• 5^4=5*5*5*5=625
• 12 years agoHelpfull: Yes(4) No(4)
• 625
  5^(3+1)=5^4
• 12 years agoHelpfull: Yes(3) No(4)
• here we have to develop those no. which are dividable by 4. For this last two digit no must be dividable by 4. That can only be in this case is (12,24,32,44,52)
  
  now we have to design the starting two digit that can be taken as
  
  5p2 that is 5*4 = 20
  
  now total no. that can be formed is 20*5 = 100.
  
  so Ans is 100.
  
  Thanks
• 9 years agoHelpfull: Yes(1) No(1)
• 5
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  5^3 = 125
  
• 10 years agoHelpfull: Yes(0) No(0)