document.write( "Question 514939: How many different numbers can be formed from the digits 0, 1, 3, 5, 7, 9 such that each number is between 2000 and 4000 ? \n" ); document.write( "
Algebra.Com's Answer #343633 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "If the numbers can be repeated:\r\n" );
document.write( "\r\n" );
document.write( "We can choose the first digit only 1 way, (it must be 3).\r\n" );
document.write( "\r\n" );
document.write( "We can choose the 2nd digit as either 0, 1, 3, 5, 7, 9.  That's 1*6 ways.\r\n" );
document.write( "\r\n" );
document.write( "For each of those 6 ways we can choose the first two digits, we can\r\n" );
document.write( "choose the 3rd digit as either 0, 1, 3, 5, 7, 9.  That's 1*6*6 ways.\r\n" );
document.write( "\r\n" );
document.write( "For each of those 1*6*6 ways we can choose the first three digits, we can\r\n" );
document.write( "choose the 4th digit as either 0, 1, 3, 5, 7, 9.  That's 1*6*6*6 ways.\r\n" );
document.write( "\r\n" );
document.write( "Answer 1*6*6*6 = 6³ = 216\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "If the numbers cannot be repeated:\r\n" );
document.write( "\r\n" );
document.write( "We can choose the first digit only 1 way, (it must be 3).\r\n" );
document.write( "\r\n" );
document.write( "We can choose the 2nd digit as either 0, 1, 5, 7, 9.  That's 1*5 ways.\r\n" );
document.write( "\r\n" );
document.write( "For each of those 5 ways we can choose the first two digits, we can\r\n" );
document.write( "choose the 3rd digit any of 4 ways.  That's 1*5*4 ways.\r\n" );
document.write( "\r\n" );
document.write( "For each of those 1*5*4 ways we can choose the first three digits, we can\r\n" );
document.write( "choose the 4th digit any of 3 ways.  That's 1*5*4*3 ways.\r\n" );
document.write( "\r\n" );
document.write( "Answer 1*5*4*3 = 60.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );