Question 410089
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