document.write( "Question 809113: How many distinguishable 6 letter words can be formed using the letters in ALASKA? \n" ); document.write( "

Algebra.Com's Answer #487409 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "If the A's were distinguishable (say different colors or different sizes or\r\n" );
document.write( "different fonts) the answer would be 6! or 720 because there are 6 letters.\r\n" );
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document.write( "However in each arrangement, say this one:\r\n" );
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document.write( "SAKALA\r\n" );
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document.write( "If the A's were colored different we could tell them apart, that is,\r\n" );
document.write( "they would be distinguishable, like these 6:\r\n" );
document.write( " \r\n" );
document.write( "SAKALA\r\n" );
document.write( "SAKALA\r\n" );
document.write( "SAKALA\r\n" );
document.write( "SAKALA\r\n" );
document.write( "SAKALA\r\n" );
document.write( "SAKALA\r\n" );
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document.write( "But since they aren't colored different, those all look the same.\r\n" );
document.write( "That is, they are indistinguishable and all look like SAKALA. So\r\n" );
document.write( "the 720 is too many.  \r\n" );
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document.write( "Now why did we know there were 6 of each arrangement that we cannot\r\n" );
document.write( "tell the difference in?  Because there are 3! or 6 ways to arrange\r\n" );
document.write( "the three A's.\r\n" );
document.write( "So that means that the 6! or 720 counts each arrangement 3! or 6\r\n" );
document.write( "times too many.  So we correct that by dividing 6! or 720 by 3! or 6\r\n" );
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document.write( " = 120 distinguishable arrangements. \r\n" );
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document.write( "Edwin

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