document.write( "Question 839174: In how many three-digit numbers are at least two of the digits the same? \n" ); document.write( "
Algebra.Com's Answer #505601 by Edwin McCravy(20056)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "They all have either exactly 2 or all 3 digits the same.\r\n" ); document.write( "\r\n" ); document.write( "There are 9 3-digit number with all 3 digits the same, 111,222,...999. \r\n" ); document.write( "\r\n" ); document.write( "The 3-digit numbers with exactly 2 digits the same are all of the form \r\n" ); document.write( "ABA, AAB, or ABB. (For example 575, 557, or 577)\r\n" ); document.write( "\r\n" ); document.write( "Therefore, we can choose the form in 3 ways.\r\n" ); document.write( "For each of those forms the A can be chosen 9 ways (A can't be 0).\r\n" ); document.write( "Then B can be chosen 9 ways (B can't be the same digit as A, \r\n" ); document.write( "but B can be 0)\r\n" ); document.write( "\r\n" ); document.write( "Answer: 9+3 = 9+243 = 252 possible 3-digit numbers with at least\r\n" ); document.write( "2 digits the same.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |