document.write( "Question 1112566: How many different words can be formed with the letters of the word \"HAHA\" \n" ); document.write( "
Algebra.Com's Answer #727630 by math_helper(2461)\"\" \"About 
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\n" ); document.write( "When I see problems like this I like to first imagine all the letters are distinct, like WXYZ.
\n" ); document.write( "With WXYZ you can make 4! = 24 unique words.\r
\n" ); document.write( "\n" ); document.write( "Obviously this over-counts by a certain amount. How much does it over-count?\r
\n" ); document.write( "\n" ); document.write( "If WX is really HH then we've over-counted by 2! times (= the number of ways WX can be uniquely arranged).
\n" ); document.write( "If YZ is really AA then we've over-counted by another 2! times.\r
\n" ); document.write( "\n" ); document.write( "So the number of unique words with HAHA is 4!/(2!*2!) = 24/4 = \"+highlight%28+6+%29+\" .\r
\n" ); document.write( "\n" ); document.write( "Since this is a small number, the unique patterns can be easily enumerated:
\n" ); document.write( "AAHH, AHAH, AHHA, HAAH, HAHA, and HHAA\r
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