document.write( "Question 579621: Thanks so much! :)\r
\n" ); document.write( "\n" ); document.write( "How many three-letter arrangements are possible using the letters of the word CANADA?\r
\n" ); document.write( "\n" ); document.write( "The problem for me is the 3-letter part. :/
\n" ); document.write( "Any help would be extremely amazing thanks! \n" ); document.write( "
Algebra.Com's Answer #371031 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If the word were, say, MONKEY instead of CANADA, the answer would be 6!\r\n" );
document.write( "arrangements. because MONKEY has all different letters.\r\n" );
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document.write( "If we could tell the A's apart in CANADA, say, if it were CANADA, the answer \r\n" );
document.write( "would also be 6! ways.  But there are fewer ways than that, because we can't\r\n" );
document.write( "tell the difference between the A's.\r\n" );
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document.write( "Let's select a typical arrangement of CANADA, say, NDAACA.\r\n" );
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document.write( "Of the 6! arrangments of CANADA. these 6 would all be counted separately \r\n" );
document.write( "among the 6! \r\n" );
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document.write( "                    NDAACA\r\n" );
document.write( "                    NDAACA\r\n" );
document.write( "                    NDAACA\r\n" );
document.write( "                    NDAACA\r\n" );
document.write( "                    NDAACA\r\n" );
document.write( "                    NDAACA\r\n" );
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document.write( "So just like NDAACA, every other arrangement is counted 6 times among\r\n" );
document.write( "the 6!, too.  The reason it is 6 times too many is because in every arrangement\r\n" );
document.write( "there are 3 places to put the red A times 2 places to put the green\r\n" );
document.write( "A times 1 place to put the blue A.  That's 3! or 6 places to put the 3 A's.\r\n" );
document.write( "So since the 6! counts each arrangement 3! or 6 times too many, we must\r\n" );
document.write( "divide the 6! by 3!  :\r\n" );
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document.write( "                         6!    6·5·4·3·2·1\r\n" );
document.write( "                         ——  = ——————————— = 6·5·4 = 120\r\n" );
document.write( "                         3!       3·2·1  \r\n" );
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document.write( "Answer: 120 ways. \r\n" );
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document.write( "Edwin
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