document.write( "Question 410089: in how many ways can the letters of the word MANAGEMENT be rearranged so that the two As do not appear together? \n" ); document.write( "

Algebra.Com's Answer #288470 by sudhanshu_kmr(1152) $\"\"$ $\"About$

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there are total 10 letters..\r
\n" ); document.write( "\n" ); document.write( "no. of M = 2\r
\n" ); document.write( "\n" ); document.write( "no. of A = 2\r
\n" ); document.write( "\n" ); document.write( "no. of N = 2\r
\n" ); document.write( "\n" ); document.write( "no. of E = 2\r
\n" ); document.write( "\n" ); document.write( "and others appear only one...\r
\n" ); document.write( "\n" ); document.write( "no. of ways to arrange these 10 letters = 10! / [ 2! * 2! * 2! * 2!] \r
\n" ); document.write( "\n" ); document.write( "= 226800\r
\n" ); document.write( "\n" ); document.write( "now, assume that two A i.e AA as single letter, total 9 letters\r
\n" ); document.write( "\n" ); document.write( "no. of ways to arrange these 9 letters where two 'A' always together\r
\n" ); document.write( "\n" ); document.write( " = 9! / [ 2! * 2! * 2! ]\r
\n" ); document.write( "\n" ); document.write( "= 45360\r
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\n" ); document.write( "\n" ); document.write( "no. of ways of arrangement where two 'A' do not come together = 226800-45360\r
\n" ); document.write( "\n" ); document.write( "= 181440\r
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