SOLUTION: in how many ways can the letters of the word MANAGEMENT be rearranged so that the two As do not appear together?

Question 410089: in how many ways can the letters of the word MANAGEMENT be rearranged so that the two As do not appear together?
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!
there are total 10 letters..
no. of M = 2
no. of A = 2
no. of N = 2
no. of E = 2
and others appear only one...
no. of ways to arrange these 10 letters = 10! / [ 2! * 2! * 2! * 2!]
= 226800
now, assume that two A i.e AA as single letter, total 9 letters
no. of ways to arrange these 9 letters where two 'A' always together
= 9! / [ 2! * 2! * 2! ]
= 45360

no. of ways of arrangement where two 'A' do not come together = 226800-45360
= 181440

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