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

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Question 1116177: 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 not allowed

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
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.              

Solved.


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