Question 1106687
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Of the 10 digits, 5 are even.  So in both cases there are 5 choices for the units digit of the 2-digit number.<br>
(a) If repetition is allowed, there are 10 choices for the tens digit after the units digit is chosen.  The total number of possible 2-digit numbers is 10*5 = 50.<br>
(b) If repetition is not allowed, there are only 9 choices left for the tens digit after the units digit is chosen.  The total number of possible 2-digit numbers is 9*5 = 45.<br>
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Oops!  I didn't spend enough time thinking about this one....<br>
The tens digit can't be 0....<br>
(a) If repetition is allowed, we have 5 choices for the units digit (any of the 5 even digits); then we have 9 choices for the tens digit (any digit except 0).  That makes 5*9 = 45 2-digit numbers.<br>
(b) If repetition is not allowed, then there are two cases to consider.<br>
If the units digit is 0, then we still have 9 digits to choose from for the tens digit; that makes 9 possible 2-digit numbers with units digit 0.<br>
If the units digit is any of the other 4 even digits, then we have only 8 choices for the tens digit (it again can't be 0; and it also can't be the same as the units digit); that makes 4*8=32 2-digit numbers with units digit 2, 4, 6, or 8.<br>
So with repetition not allowed, the total number of possible 2-digit numbers is 9+32=41.