3 votes 3 votes 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? Quantitative Aptitude gatebook combinatory + – Purple asked Feb 7, 2017 • retagged Jun 27, 2017 by Arjun Purple 955 views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Rahul Jain25 commented Feb 7, 2017 reply Follow Share You have to arrange all leters. I was getting 7!/(6) but no option matched. 0 votes 0 votes Quixote commented Apr 15, 2017 reply Follow Share (7!/2!)(All) / (3!/2!)(discount) = 7!/3! 0 votes 0 votes Please log in or register to add a comment.
Best answer 6 votes 6 votes 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) sudoankit answered Feb 7, 2017 • selected Feb 7, 2017 by Arjun sudoankit comment Share Follow See all 7 Comments See all 7 7 Comments reply Shubhanshu commented Mar 16, 2017 reply Follow Share but u didn't cover the cases like "A M I A" which is also a valid string. 1 votes 1 votes Rahul Jain25 commented Mar 16, 2017 reply Follow Share I also have same doubt. @Subhanshu what answer are you getting?? 0 votes 0 votes Shubhanshu commented Mar 16, 2017 reply Follow Share none of the option is matching... what is your answer??? 0 votes 0 votes Rahul Jain25 commented Mar 16, 2017 reply Follow Share I am getting 7!/3! 1 votes 1 votes Vicky rix commented Mar 16, 2017 reply Follow Share @ Shubhanshu same doubt here 1 votes 1 votes Shubhanshu commented Mar 16, 2017 reply Follow Share getting 840 which is equivalent to 7!/6 after considering all cases. 0 votes 0 votes itsvkp1 commented Aug 24, 2017 reply Follow Share this given answer is wrong , please correct it if anyone can.. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes 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. Chhotu answered Oct 17, 2017 Chhotu comment Share Follow See 1 comment See all 1 1 comment reply VS commented Oct 23, 2017 reply Follow Share 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? 1 votes 1 votes Please log in or register to add a comment.