document.write( "Question 1021854: How many 8 digit numbers are there with 3 different digits,
\n" ); document.write( "one appearing twice and the other two appearing 3 times each.
\n" ); document.write( "Assume zero cannot be used at all. \n" ); document.write( "

Algebra.Com's Answer #637590 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

There are 9C3 ways to choose the 3 digits.\r\n" );
document.write( "\r\n" );
document.write( "Of those 3 choose the digit to be used only twice 3C1 ways. \r\n" );
document.write( "\r\n" );
document.write( "There are 8 places in an 8-digit number for the digits to go.\r\n" );
document.write( "\r\n" );
document.write( "Choose the 2 places for the digit to be used twice in 8C2 ways.\r\n" );
document.write( "That leaves 6 places for the larger of the 2 remaining digits.\r\n" );
document.write( "Choose the 3 places for the larger remaining digit to go in 6C3 ways.\r\n" );
document.write( "That leaves 3 places for the smaller remaining digit.\r\n" );
document.write( "Choose the places for the smallest digits to go in 3C3 or 1 way. \r\n" );
document.write( "(Only 1 way, because there are only 3 places left for the \r\n" );
document.write( "smallest digit).\r\n" );
document.write( "\r\n" );
document.write( "Answer: (9C3)(3C1)(8C2)(6C3)(3C3) = 141120 ways \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );