document.write( "Question 1197177: How many arrangements of the letters in KILLNACOUNTING are possible?
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Algebra.Com's Answer #830330 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "There are 14 letters in \"KILLNACOUNTING\"
\n" ); document.write( "The letters that repeat are I, L, and N.\r
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\n" ); document.write( "\n" ); document.write( "If we could distinguish between the repeated letters, then we'd have 14! = 14*13*12*11*10*9*8*7*6*5*4*3*2*1 = 87,178,291,200 different permutations.
\n" ); document.write( "The exclamation mark stands for a factorial. We start at 14 and count our way down to 1 multiplying along the way.
\n" ); document.write( "Many calculators have an exclamation mark button to make this calculation fairly quick. Meaning you can avoid typing in 14 times 13 times ... all the way down to 1.\r
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\n" ); document.write( "\n" ); document.write( "Anyways, that very large number would be the answer if we could tell those repeated letters apart.
\n" ); document.write( "But we can't tell them apart.
\n" ); document.write( "There are...
\n" ); document.write( "2 I's
\n" ); document.write( "2 L's
\n" ); document.write( "3 N's
\n" ); document.write( "So we must divide that massive number by 2!*2!*3! = 2*2*6 = 24 to correct for the fact we cannot distinguish these letters from one another.\r
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\n" ); document.write( "\n" ); document.write( "(87,178,291,200)/(24) = 3,632,428,800
\n" ); document.write( "This is approximately 3.63 billion\r
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\n" ); document.write( "\n" ); document.write( "Answer: 3,632,428,800
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