Ive been asking for a long time and nobody has answered so please help me out here :(
1) License plate numbers in poglandia used to consist of 5 distinct digits. Due to an increase in population, poglandia started to allow license plates to have any 5-digit string, even if some digits are the same. How many more license plates are available because of this change?
2) Each of the digits 1,2,3,4,5,6 is used exactly once in forming the 3-digit integers X and Y. How many possible values of X+Y are there if |X-Y|=111?
3) The product of all digits of positive integer M is 105 How many such Ms are there with distinct digits?
4) What fraction of all the 10-digit numbers with distinct digits have the property that the sum of every pair of neighboring digits is odd?