How many 8 digit numbers formed using 1,2,3,4,5 with repetition are divisible by 4?
97657
97656
78125
31250

• last 2 digits can be 12,24,32,44,52 .... 5
  8 digit numbers formed using 1,2,3,4,5 with repetition which are divisible by 4 =5* 5^6 = 5^7 = 78125
• 12 years agoHelpfull: Yes(7) No(5)
• 1 st 6 digit can be formed in 5^6 ways and the last two digit can be formed in 5*2 ways e.g(12,14,22,24,32,34,42,44,52,54)
  i.e 5^6*5*2=156250
• 12 years agoHelpfull: Yes(1) No(6)
• You have 5 symbols that are repeated 8 times, but your example is not an 8 digit number that is made up of the symbols given. I'm going to assume that the number is a typo and you really meant 5 symbols, so it is (5^8)-1 possible numbers.
  
  390624 numbers. Now, how many of those numbers are divisible by 4? In the lowest digit, only 2 of 5 numbers are divisible by 2, and half, or 1 of those, on average would be divisible by 4. That comes to 78124 and a fraction, and the number 78125 is the only number close to that one.
  
  Here is an entire J program that generates and counts the symbols that are divisible by 4:
  
  +/0=4|(8$10)#.1+(8$5)#:i.5^8
  78125
• 11 years agoHelpfull: Yes(1) No(0)
• last 2 digits can be 12,24,32,44,52 .... 5
  so 5^(8-1)=>5^7
  =78125
• 12 years agoHelpfull: Yes(0) No(0)
• 5^6*5=78125
• 11 years agoHelpfull: Yes(0) No(0)