document.write( "Question 1205467: In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty? \n" ); document.write( "

Algebra.Com's Answer #842289 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "In how many ways can you distribute 8 indistinguishable balls among 2 distinguishable boxes,
\n" ); document.write( "if at least one of the boxes must be empty?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let the boxes be B1 and B2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It it obvious, that under given condition, EITHER box B1 OR box B2 must be empty.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If box B1 is empty, then all 8 indistinguishable balls are in box B2: so,\r\n" );
document.write( "there is only one such distribution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If box B2 is empty, then all 8 indistinguishable balls are in box B1: so,\r\n" );
document.write( "there is only one such distribution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In all, there are 1 + 1 = 2 such distinguishable distributions.    ANSWER\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" ); document.write( "

\n" );