document.write( "Question 658654: find the number of ways of selecting four letters from the word 'EXAMINATION'.ANSWER IS 136 PLS SOLVE THIS THANK U \n" ); document.write( "

Algebra.Com's Answer #410407 by kevwill(135) $\"\"$ $\"About$

You can put this solution on YOUR website!
Actually, the answer is 131.\r
\n" ); document.write( "\n" ); document.write( "For an excellent, detailed description of the theory behind the solution, please see http://mathforum.org/library/drmath/view/56197.html\r
\n" ); document.write( "\n" ); document.write( "I sorted the letters of the word EXAMINATION by frequency of occurrence to get AAIINNEMOTX. That told me we are looking for the number of 4-combinations of the set (2,2,2,1,1,1,1,1). \r
\n" ); document.write( "\n" ); document.write( "We can use the generating function $\"%281+%2B+x+%2B+x%5E2%29%5E3%2A%281+%2B+x%29%5E5\"$ and find the coefficient of the resulting $\"x%5E4\"$ term.\r
\n" ); document.write( "\n" ); document.write( "When multiplied out, the expanded generating function is:
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and the coefficient of the $\"x%5E4\"$ term is 131. Thus, there are 131 ways to select four letters from the word \"EXAMINATION\"\r
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