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In how many ways of the distinct permutations of the letters in 'Mississippi' do the four 'i' not come together

Answer :

it is same as the (total no of permutations - permutations in which all 4 i's come together) = 11!/(4!*2!*4!*) - 8!/(4!*2!)  
since total no. of digits are 11 
in which i =4 s=4 p=2
there fore total permutations =11!/4!4!2!
                                         =34650
now we take all i's together hen total no will be 8 as we count all i's to be 1
now total permutations if all i's come together =8!/4!2!
                                                                  =840
 therefore total permutations when all is not come together =34650-840
                                                                                     =33810

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