Question 1169539: Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to determine how many three digit numbers are possible when there are NO restrictions and numbers CAN be repeated.
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to determine how many three digit numbers are possible
when there are NO restrictions and  digits CAN be repeated.
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Any non-zero digit in the left-most position: 9 options;
any of 10 digit in the next (2nd) position: 10 options;
any of 10 digit in the next (3rd) position: 10 options.
These selections are independent for each of the 3 positions - - - so, according to the Fundamental Counting Principle,
there are 9*10*10 = 900 different three-digit numbers.
You can calculate it in other way by noticing that 900 is 1000 (all possible 3-digit combinations,
including 0 in the left-most position) _MINUS_ 3-digit words starting from 0.
Solved and answered using two methods for your better understanding.
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