document.write( "Question 1183044: How many ways can we select three books each from a different subject from a set of six distinct history books, nine distinct classics books, seven distinct law books, and four distinct education books? \n" ); document.write( "

Algebra.Com's Answer #813187 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "How many ways can we select three books each from a different subject
\n" ); document.write( "from a set of six distinct history books, nine distinct classics books,
\n" ); document.write( "seven distinct law books, and four distinct education books?
\n" ); document.write( "~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "We have the sets \r\n" );
document.write( "\r\n" );
document.write( "    - H (history, 6 books)\r\n" );
document.write( "\r\n" );
document.write( "    - C (classic, 9 books)\r\n" );
document.write( "\r\n" );
document.write( "    - L (law, 7 books)\r\n" );
document.write( "\r\n" );
document.write( "    - E (educational, 4 books).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We can select 3 different subject books from the set H U C U L by 6*9*7 = 378 ways.\r\n" );
document.write( "\r\n" );
document.write( "We can select 3 different subject books from the set H U C U E by 6*9*4 = 216 ways.\r\n" );
document.write( "\r\n" );
document.write( "We can select 3 different subject books from the set H U L U E by 6*7*4 = 168 ways.\r\n" );
document.write( "\r\n" );
document.write( "We can select 3 different subject books from the set C U L U E by 9*7*7 = 252 ways.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Doing this way, we counted all possible combinations of 3 different subject books.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the answer to the problem's question is the sum  378 + 216 + 168 + 252 = 1014 different ways.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved and carefully explained.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );