document.write( "Question 564366: how many different ways can i rearrange 26 apples in groups of 6 ? \n" ); document.write( "

Algebra.Com's Answer #365344 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
how many different ways can i rearrange 26 apples in groups of 6 ?
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "I disagree with the other tutor's answer.\r\n" );
document.write( "\r\n" );
document.write( "4 groups of 6 means you use only 24 of the 26 apples, and so you have \r\n" );
document.write( "to leave two apples behind.  \r\n" );
document.write( "\r\n" );
document.write( "First let's count the number of ways in which the 4 groups are\r\n" );
document.write( "ordered: first group, second group, third group, and fourth group.\r\n" );
document.write( "Then we'll divide by 4! to get rid of the extra ones, since order\r\n" );
document.write( "doesn't matter.\r\n" );
document.write( "\r\n" );
document.write( "The ways to choose the two to leave behind are C(26,2)\r\n" );
document.write( "For each of those ways to leave two behind,\r\n" );
document.write( "there are C(24,6) ways to choose the first group, then\r\n" );
document.write( "there are C(18,6) ways to choose the second group, then\r\n" );
document.write( "there are C(12,6) ways to choose the third group, then\r\n" );
document.write( "there are C(6,6) (or 1 way) to choose the 4th group.\r\n" );
document.write( "\r\n" );
document.write( "That's C(26,2)C(24,6)C(18,6)C(12,6)C(6,6) ways if the\r\n" );
document.write( "groups were in a certain order.  But since order doesn't\r\n" );
document.write( "matter, ordering them causes each to be counted 4! times \r\n" );
document.write( "too many, so we divide by 4!:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.12642348×10¹³\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );