document.write( "Question 1188402: How many 9s are there at the end of the number (60!-50!-1)?
\n" ); document.write( "(n!=n*(n-1)*(n-2)*...3*2*1) \n" ); document.write( "

Algebra.Com's Answer #819510 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "# of 0's at the end of 60!\r\n" );
document.write( "  60/5 = 12\r\n" );
document.write( "  12/5 =  2\r\n" );
document.write( " -----------\r\n" );
document.write( "         14\r\n" );
document.write( "\r\n" );
document.write( "# of 0's at the end of 50!\r\n" );
document.write( "  50/5 = 10\r\n" );
document.write( "  10/5 =  2\r\n" );
document.write( " -----------\r\n" );
document.write( "         12

\n" ); document.write( "There are 14 trailing 0's in 60! and only 12 in 50!, so 60!-50! has 12 trailing 0's.

\n" ); document.write( "That means 60!-50!-1 has 12 trailing 9's.

\n" ); document.write( "Using the pari calculator, available online: 60!-50!-1 = 8320987112741390113862247981509986337141564440296477108071636127449087 999 999 999 999

\n" ); document.write( "which indeed has 12 trailing 9's

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

\n" );