document.write( "Question 960370: how to find the total number of 9- digit numbers having all different digits \n" ); document.write( "
Algebra.Com's Answer #586891 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "There are 10 digits, 0,1,2,3,4,5,6,7,8,9\r\n" ); document.write( "\r\n" ); document.write( "We can choose the first digit any of 9 ways (we cannot choose 0\r\n" ); document.write( "for the 1st digit in a 9-digit number).\r\n" ); document.write( "\r\n" ); document.write( "For each of those we can choose the 2nd digit any of 9 ways,\r\n" ); document.write( "for there are 9 remaining digits that weren't chosen for the \r\n" ); document.write( "1st digit. (we can now choose 0 as one of the digits other \r\n" ); document.write( "than the first).\r\n" ); document.write( "\r\n" ); document.write( "For each of those we can choose the 3rd digit any of 8 ways,\r\n" ); document.write( "for there are 8 remaining digits that weren't chosen for the \r\n" ); document.write( "1st or 2nd digit.\r\n" ); document.write( "\r\n" ); document.write( "For each of those we can choose the 4th digit any of 7 ways,\r\n" ); document.write( "for there are 7 remaining digits that weren't chosen for the \r\n" ); document.write( "1st or 2nd or 3rd digit.\r\n" ); document.write( "\r\n" ); document.write( "For each of those we can choose the 5th digit any of 6 ways,\r\n" ); document.write( "for there are 6 remaining digits that weren't chosen for the \r\n" ); document.write( "1st or 2nd or 3rd or 4th digit.\r\n" ); document.write( "\r\n" ); document.write( "For each of those we can choose the 6th digit any of 5 ways,\r\n" ); document.write( "for there are 5 remaining digits that weren't chosen for the \r\n" ); document.write( "1st or 2nd or 3rd or 4th or 5th digit.\r\n" ); document.write( "\r\n" ); document.write( "For each of those we can choose the 7th digit any of 4 ways,\r\n" ); document.write( "for there are 4 remaining digits that weren't chosen for the \r\n" ); document.write( "1st or 2nd or 3rd or 4th or 5th or 6th digit.\r\n" ); document.write( "\r\n" ); document.write( "For each of those we can choose the 8th digit any of 3 ways,\r\n" ); document.write( "for there are 3 remaining digits that weren't chosen for the \r\n" ); document.write( "1st or 2nd or 3rd or 4th or 5th or 6th or 7th digit.\r\n" ); document.write( "\r\n" ); document.write( "For each of those we can choose the 9th digit either of 2 ways,\r\n" ); document.write( "for there are 2 remaining digits that weren't chosen for the \r\n" ); document.write( "1st or 2nd or 3rd or 4th or 5th or 6th or 7th or 8th digit.\r\n" ); document.write( "\r\n" ); document.write( "Mutily all those numbers of ways together:\r\n" ); document.write( "\r\n" ); document.write( "9 = 3265920 9 digit numbers with all different \r\n" ); document.write( "digits.\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |