Question

By using 1,2,3,4,5,how many 5 digit no. can be formed which is divisible by 4,repetation of no. is allowed?

Answer 1

for first 3 places we have 5*5*5=125 combinations

next 2 possibilities are 12,24,32,44,52

so 125*5=625 numbers

thanks

Answer 2

Last two digits must be  ( 04,12,16,20,24,32,36 , 40, 52, 56, 60 , 64 )  in order to be from ( 0 - 6 ) be divisible by 4 and not be repeated.  4 cases where 0 is in last 2 digits ( 04,20,40,60 ) the other 3 digits filled by  4 ( 5 x 4 x 3 ) choices = 240  8 ways that don’t use 0 and since 0 can’t be the first digit  ( 12 , 16, 24, 32, 36, 52, 56, 64 )  8 ( 4 x 4 x 3 ) = 384  240 + 384 = 624