document.write( "Question 1024628: How many 4 digit numbers can be formed with
\n" ); document.write( "the 10 digit ie (.0,1,2,3,4,5,6,7,8,9) if
\n" ); document.write( "(a) repetitions are allowed.
\n" ); document.write( "(b) repetitions are not allowed.
\n" ); document.write( "(c) last digit must be zero and repetition are not allowed. \n" ); document.write( "
Algebra.Com's Answer #640066 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
How many 4 digit numbers can be formed with the
\n" ); document.write( "10 digits i.e., (.0,1,2,3,4,5,6,7,8,9) if \r
\n" ); document.write( "\n" ); document.write( "(a) repetitions are allowed.
\n" ); document.write( "
\r\n" );
document.write( "You can do this two ways.\r\n" );
document.write( "First way:\r\n" );
document.write( "There are 9999 integers from 1 to 9999 inclusive.\r\n" );
document.write( "There are 999 integers from 1 to 999 inclusive which \r\n" );
document.write( "have fewer than 4 digits.  So there are 9999-999 or\r\n" );
document.write( "9000 4 digit-numbers.\r\n" );
document.write( "\r\n" );
document.write( "Second way:\r\n" );
document.write( "Choose the first digit 9 ways from {1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "the first digit cannot be 0.\r\n" );
document.write( "Choose the second digit any of 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the third digit any of 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "Choose the fourth digit any of 10 ways {0,1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "\r\n" );
document.write( "That's 9*10*10*10 = 9000 4-digit numbers\r\n" );
document.write( "

\n" ); document.write( "(b) repetitions are not allowed.
\n" ); document.write( "
\r\n" );
document.write( "Choose the first digit 9 ways from {1,2,3,4,5,6,7,8,9}\r\n" );
document.write( "the first digit cannot be 0.\r\n" );
document.write( "Choose the second digit any of 9 ways.\r\n" );
document.write( "It can be 0.\r\n" );
document.write( "Choose the third digit any of 8 ways.\r\n" );
document.write( "Choose the fourth digit any of 7 ways.\r\n" );
document.write( "\r\n" );
document.write( "That's 9*9*8*7 = 4536 ways.\r\n" );
document.write( "

\n" ); document.write( "(c) last digit must be zero and repetition are not allowed.
\n" ); document.write( "
\r\n" );
document.write( "Choose the last digit 1 way.\r\n" );
document.write( "Choose the first digit any of 9 ways.\r\n" );
document.write( "Choose the second digit any of 8 ways.\r\n" );
document.write( "Choose the third digit any of 7 ways.\r\n" );
document.write( "\r\n" );
document.write( "That's 1*9*8*7 = 504 ways.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );