The 120 permutations of MAHES are arranged in dictionary order, as if each were an ordinary five-letter word. The last letter of the 86th word in the list is

(A) A
(B) H
(C) S
(D) E
(E) M

Question

The 120 permutations of MAHES are arranged in dictionary order, as if each were an ordinary five-letter word. The last letter of the 86th word in the list is  
    
(A) A  
(B) H  
(C) S  
(D) E  
(E) M

Jaideep Hooda · Answer

The answer would be option (D)

AEHMS

With A as the first word, total words = 4*3*2*1 = 24
Similarly, with E as the first word, total words = 4*3*2*1 = 24
Similarly, with H as the first word, total words = 4*3*2*1 = 24

That makes a total of 72

Now, let's come to M as the first letter and:

i) A as the second letter, total words = 3*2*1 = 6 (that makes a total of 78)
ii) E as the second letter, total words = 3*2*1 = 6 (that makes a total of 84)

With H as the second letter:

85th word is MHAES
86th word is MHASE

So, 'E' is the last letter of the 86th word.

The 120 permutations of MAHES are arranged in dictionary order, as if each were an ordinary five-letter word. The last.

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