document.write( "Question 1185054: There are 4 copies of Statistics book, 5 copies of Science book, and 3 copies of English book. In how many ways can they be arranged on a shelf? \n" ); document.write( "

Algebra.Com's Answer #815778 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "There are 4 copies of Statistics book, 5 copies of Science book,
\n" ); document.write( "and 3 copies of English book. In how many ways can they be arranged on a shelf?
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Based on context, I interpret the given part as if the copies of each kind are undistinguishable.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Then the question is: how many DISTINGUISHABLE arrangements are there in this situation ?\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The total number of books is  4+5+3 = 12;  the multiplicities are  4, 5 and 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use the formula for the number of distinguishable arrangements and get the number\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     =  = 27720.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The number of distinguishable arrangements is 27720.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Arranging elements of sets containing indistinguishable elements \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Combinatorics: Combinations and permutations\". \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );