document.write( "Question 867987: How many three-digit odd numbers are possible if the leftmost digit cannot be zero?
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Algebra.Com's Answer #524918 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! How many three-digit odd numbers are possible if the leftmost digit cannot be zero? \n" ); document.write( " \r\n" ); document.write( "\r\n" ); document.write( "Two ways:\r\n" ); document.write( "\r\n" ); document.write( "First way:\r\n" ); document.write( "\r\n" ); document.write( "There are 9 choices for the first digit: 1,2,3,4,5,6,7,8,9\r\n" ); document.write( "There are 10 choices for the second digit: 0,1,2,3,4,5,6,7,8,9\r\n" ); document.write( "There are 5 choices for the third digit: 1,3,5,7,9\r\n" ); document.write( "\r\n" ); document.write( "That's 9×10×5 = 450\r\n" ); document.write( "\r\n" ); document.write( "---------------------------------------\r\n" ); document.write( "\r\n" ); document.write( "Second way:\r\n" ); document.write( "\r\n" ); document.write( "That's the arithmetic sequence \r\n" ); document.write( "\r\n" ); document.write( "101,103,...,997,999\r\n" ); document.write( "\r\n" ); document.write( "with a1 = 101, an = 999, and d=2\r\n" ); document.write( "\r\n" ); document.write( "an = a1 + (n-1)d\r\n" ); document.write( "\r\n" ); document.write( "999 = 101 + (n-1)2\r\n" ); document.write( "\r\n" ); document.write( "Solve for n, get n = 450.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |