SOLUTION: How many four digits number can be formed with the 10 digits 0-9 a) If repetitions are allowed b) Repetitions are not allowed c) The last digit must be zero and repetitions are

a)  Answer.  9000 four digit numbers.

             It is the full number of existing 4-digit numbers, 

             and it is how many four digits number can be formed with the 10 digits 0-9,  if repetitions are allowed.



b)  Answer.  9*9*8*7 = 4536.


              Very first (the left-most) digit can be any of 9 digits from 1 to 9
                   (zero is excluded in this position);

              Next digit can be any of 9 remaining digits (zero is included in this position)

              Next digit can be any of 8 remaining digits;

              Next (and the last) digit can be any of 7 remaining digits.


              In all, there are  9*9*8*7 opportunities.



b)  Answer.  9*8*7 = 504.


              The digit zero is fixed in the "ones" position.

              Very first (the left-most) digit can be any of 9 digits from 1 to 9
                   (zero is excluded in this position);

              Next digit can be any of 8 remaining digits;

              Next digit can be any of 7 remaining digits.


              In all, there are  9*8*7 opportunities.