document.write( "Question 356905: In how many ways can five math books and four novels be placed on a bookshelf if the math books must be together? \n" ); document.write( "
Algebra.Com's Answer #254858 by Edwin McCravy(20060) $\"\"$ $\"About$
You can put this solution on YOUR website!
\r\n" );
document.write( "| | | | | |N|N|N|N|\r\n" );
document.write( "|M|M|M|M|M|O|O|O|O|\r\n" );
document.write( "|A|A|A|A|A|V|V|V|V|\r\n" );
document.write( "|T|T|T|T|T|E|E|E|E| \r\n" );
document.write( "|H|H|H|H|H|L|L|L|L|  \r\n" );
document.write( "\r\n" );
document.write( "For the above way of placing the books, there are 5! ways to\r\n" );
document.write( "arranging the math books, and for each of those ways there\r\n" );
document.write( "are 4! ways of arranging the novels.  That's 5!4! ways for\r\n" );
document.write( "having all 5 math books on the left and all four novels on\r\n" );
document.write( "the right.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "|N| | | | | |N|N|N|\r\n" );
document.write( "|O|M|M|M|M|M|O|O|O|\r\n" );
document.write( "|V|A|A|A|A|A|V|V|V|\r\n" );
document.write( "|E|T|T|T|T|T|E|E|E|\r\n" );
document.write( "|L|H|H|H|H|H|L|L|L|\r\n" );
document.write( "\r\n" );
document.write( "For the above way of placing the books, there are 5! ways to\r\n" );
document.write( "arranging the math books, and for each of those ways there\r\n" );
document.write( "are 4! ways of arranging the novels.  That's 5!4! ways for\r\n" );
document.write( "having 1 novel on the left, then the 5 math books, then 4 \r\n" );
document.write( "novels on the right.\r\n" );
document.write( "\r\n" );
document.write( "|N|N| | | | | |N|N|\r\n" );
document.write( "|O|O|M|M|M|M|M|O|O|\r\n" );
document.write( "|V|V|A|A|A|A|A|V|V|\r\n" );
document.write( "|E|E|T|T|T|T|T|E|E|\r\n" );
document.write( "|L|L|H|H|H|H|H|L|L|\r\n" );
document.write( "\r\n" );
document.write( "For the above way of placing the books, there are 5! ways to\r\n" );
document.write( "arranging the math books, and for each of those ways there\r\n" );
document.write( "are 4! ways of arranging the novels.  That's 5!4! ways for\r\n" );
document.write( "having 2 novels on the left, then the 5 math books, then 2 \r\n" );
document.write( "novels on the right.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "|N|N|N| | | | | |N|\r\n" );
document.write( "|O|O|O|M|M|M|M|M|O|\r\n" );
document.write( "|V|V|V|A|A|A|A|A|V|\r\n" );
document.write( "|E|E|E|T|T|T|T|T|E|\r\n" );
document.write( "|L|L|L|H|H|H|H|H|L|\r\n" );
document.write( "\r\n" );
document.write( "For the above way of placing the books, there are 5! ways to\r\n" );
document.write( "arranging the math books, and for each of those ways there\r\n" );
document.write( "are 4! ways of arranging the novels.  That's 5!4! ways for\r\n" );
document.write( "having 3 novels on the left, then the 5 math books, then 1 \r\n" );
document.write( "novels on the right.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "|N|N|N|N| | | | | |\r\n" );
document.write( "|O|O|O|O|M|M|M|M|M|\r\n" );
document.write( "|V|V|V|V|A|A|A|A|A|\r\n" );
document.write( "|E|E|E|E|T|T|T|T|T|\r\n" );
document.write( "|L|L|L|L|H|H|H|H|H|\r\n" );
document.write( "\r\n" );
document.write( "For the above way of placing the books, there are 5! ways to\r\n" );
document.write( "arranging the math books, and for each of those ways there\r\n" );
document.write( "are 4! ways of arranging the novels.  That's 5!4! ways for\r\n" );
document.write( "having all four novels on the left and all five math books on\r\n" );
document.write( "the right.\r\n" );
document.write( "\r\n" );
document.write( "That's a total of 5*5!*4! = 14400\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );