document.write( "Question 1021790: How many eight digit numbers are there in which appears 3
\n" ); document.write( "different digits where the largest digits appears twice
\n" ); document.write( "and the other two appears three times each. Assume 0
\n" ); document.write( "cannot be used at all. \n" ); document.write( "

Algebra.Com's Answer #637561 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( "Each of those choices is made up of a largest digit, \r\n" );
document.write( "a middle-sized digit, and a smallest digit.\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 largest digit to go in 8C2 ways.\r\n" );
document.write( "That leaves 6 places for the middle-sized digit.\r\n" );
document.write( "Choose the 3 places for the middle-sized digit to go in 6C3 ways.\r\n" );
document.write( "That leaves 3 places for the smallest digit.\r\n" );
document.write( "Choose the places for the smallest digits to go in 3C3 of 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)(8C2)(6C3)(3C3) = 47040 \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );