gatebook

Question

How many ways are there for arranging letters of the word AMAZING such that the 'I' appears between the two 'A's?

(A) 5! ways

(B) 7! ways

(C) 8! ways

(D) 4! ways

Note: AMZIA is valid and AIA is also valid right?

Comments

You have to arrange all leters. I was getting 7!/(6) but no option matched.

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(7!/2!)(All) / (3!/2!)(discount) = 7!/3!

Answer 1

Consider 'AIA'  to be a character. Now AMAZING becomes MZNG(AIA).

Now all are unique, ( M, Z, N, G and {AIA} ) = 5 characters thus we can have $ 5! $ combinations.

Option : (A)

Comments

@ Shubhanshu same doubt here 

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getting 840 which is equivalent to 7!/6 after considering all cases.

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this given answer is wrong , please correct it if anyone can..

Answer 2

Notice ->  AMZIA is valid and AIA is also valid.

So total number of permutation of word is 7!/2! = 2520.

In all such cases AIA could come in three forms AAI, AIA or IAA. All are equally likely so I think correct answer is 2520/3 = 840.

Comments

Sorry for my late reply was bsy :)

Yes i am also getting 840 as answer but could not understand why are u dividing by 3?