document.write( "Question 229152: how many 3 digit number can we do out of these numbers {0,1,2,3,4,5,6}
\n" ); document.write( "that are greater than 330.(repetition is allowed) \n" ); document.write( "
Algebra.Com's Answer #169959 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
how many 3 digit number can we do out of these numbers {0,1,2,3,4,5,6}
\n" ); document.write( "that are greater than 330.(repetition is allowed)
\n" ); document.write( "
\r\n" );
document.write( "The smallest one allowable is 331.\r\n" );
document.write( "\r\n" );
document.write( "All must begin with 3,4,5, or 6.  However, finding how many begin\r\n" );
document.write( "with 3 is different from finding how many are langer.  Also, of those\r\n" );
document.write( "beginning with 3, finding how many begin with 33 is different from \r\n" );
document.write( "finding how many begin with 34, 35, or 36.\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "First we count all the three digit numbers beginning with 33:\r\n" );
document.write( "\r\n" );
document.write( "We can choose only 1, 2, 3, 4, 5, or 6 for the third digit.  That's 6\r\n" );
document.write( "choices for the third digit of those beginning with 33.\r\n" );
document.write( "\r\n" );
document.write( "So there are 6 allowable 3-digit numbers beginning with 33.  These are\r\n" );
document.write( "\r\n" );
document.write( "331, 332, 333, 334, 335, or 336.\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Next we must find how many begin with 34, 35, or 36.\r\n" );
document.write( "\r\n" );
document.write( "We can choose the second digit any of 3 ways (either 4, 5 or 6)\r\n" );
document.write( "\r\n" );
document.write( "We can then choose the third digit any of the total 7 ways.\r\n" );
document.write( "\r\n" );
document.write( "That's 3x7 or 21 allowable 3-digit numbers beginning with 34, 35, or 36\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Finally we must find how many 3-digit numbers beginning with 4, 5, or 6\r\n" );
document.write( "\r\n" );
document.write( "We can choose the first digit any of 3 ways (4, 5, or 6)\r\n" );
document.write( "\r\n" );
document.write( "We can choose the second digit any of the 7 ways.\r\n" );
document.write( "\r\n" );
document.write( "We can choose the third digit and of the 7 ways.\r\n" );
document.write( "\r\n" );
document.write( "That's 3x7x7 or 147 allowable 3-digit numbers beginning with 4,5, or 6\r\n" );
document.write( "\r\n" );
document.write( "Answer: 6 + 21 + 147 = 174\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );