document.write( "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.\r
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Algebra.Com's Answer #794318 by ikleyn(52781)![]() ![]() You can put this solution on YOUR website! . \n" ); document.write( "Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to determine how many three digit numbers are possible \n" ); document.write( "when there are NO restrictions and \n" ); document.write( "~~~~~~~~~~~~~~~~~~\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " Pay attention on how I edited your post\r \n" ); document.write( "\n" ); document.write( " and learn to write correctly.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( "Any non-zero digit in the left-most position: 9 options;\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "any of 10 digit in the next (2nd) position: 10 options;\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "any of 10 digit in the next (3rd) position: 10 options.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "These selections are independent for each of the 3 positions - - - so, according to the Fundamental Counting Principle,\r\n" ); document.write( "\r\n" ); document.write( "there are 9*10*10 = 900 different three-digit numbers.\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "You can calculate it in other way by noticing that 900 is 1000 (all possible 3-digit combinations, \r\n" ); document.write( "including 0 in the left-most position) _MINUS_ 3-digit words starting from 0.\r\n" ); document.write( "\r \n" ); document.write( "\n" ); document.write( "Solved and answered using two methods for your better understanding.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |