document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106687>Question 1106687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many two-digit even numbers can you form using the digits 0, 1 , 2, 3, 4, 5, 6, 7, 8, 9?<BR>\n" );
document.write( "a. repetition is allowed<BR>\n" );
document.write( "b. no repetition </SPAN>\n" );
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document.write( "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><BR>\n" );
document.write( "(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><BR>\n" );
document.write( "(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><BR>\n" );
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document.write( "Oops!  I didn't spend enough time thinking about this one....<br><BR>\n" );
document.write( "The tens digit can't be 0....<br><BR>\n" );
document.write( "(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><BR>\n" );
document.write( "(b) If repetition is not allowed, then there are two cases to consider.<br><BR>\n" );
document.write( "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><BR>\n" );
document.write( "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><BR>\n" );
document.write( "So with repetition not allowed, the total number of possible 2-digit numbers is 9+32=41. </SPAN>\n" );
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