document.write( "Question 1116159: What is the probability that a randomly chosen four-digit number contains no repeated digits? \n" ); document.write( "

Algebra.Com's Answer #730989 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "1.  The full space of events consists of 9999-999 = 9000 elements (4-digit numbers).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  Of them, the favorable sub-space are those 4-digit numbers that have no repeating digits.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        The number of elements in this sub-space = 9*9*8*7\r\n" );
document.write( "\r\n" );
document.write( "            (any of 9 digits from 1 to 9 in the left-most position;   (0 (zero) is excluded);\r\n" );
document.write( "\r\n" );
document.write( "             any of remaining 9 digits in the next position;   (0 is included !)\r\n" );
document.write( "\r\n" );
document.write( "                  . . . and so on . . . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.  Hence, the probability under the question is   = 0.504 = 50.4%.\r\n" );
document.write( "

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

\n" );