document.write( "Question 1029840: How many ways can the letters in the word AGATHIST be rearranged?
\n" ); document.write( "Any help will be appreciated! \n" ); document.write( "
Algebra.Com's Answer #644778 by mathmate(429)\"\" \"About 
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\n" ); document.write( "Question:
\n" ); document.write( "How many ways can the letters in the word AGATHIST be rearranged?
\n" ); document.write( "Any help will be appreciated!
\n" ); document.write( "
\n" ); document.write( "Solution:\r
\n" ); document.write( "\n" ); document.write( "the number of permutations is given by
\n" ); document.write( "n!/(n1!n2!n3!...nk!)
\n" ); document.write( "where each of n1, n2... is the number of occurrences of each letter.
\n" ); document.write( "Making a count of each letter:
\n" ); document.write( "A 2
\n" ); document.write( "G 1
\n" ); document.write( "H 1
\n" ); document.write( "I 1
\n" ); document.write( "S 1
\n" ); document.write( "T 2
\n" ); document.write( "total 8.
\n" ); document.write( "So the number of permutations is
\n" ); document.write( "8!/(2!1!1!1!1!2!)=40320/4=10080
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\n" ); document.write( "The same formula can also be used to solve problems of permutation of multiple coloured balls.\r
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