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

Question

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

Tardigrade Admin · Accepted Answer

The first 24=4 ! words begin with A, the next 24 begin with E and the next 24 begin with H. So the 86 text th begins with M and it is the 86-72=14 text th such word. The first 6 words that begin with M begin with M A and the next 6 begin with M E. So the desired word begins with M H and it is the second such word. The first word that begins with M H is MHAES, the second is MHASE. Thus, E is the letter we seek.

Q. The $120$ permutations of $M A H ES$ are arranged in dictionary order, as if each were an ordinary five-letter word. The last letter of the $8 6^{th}$ word in the list is

$A$

$H$

$S$

$E$

Q. 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

H

S

E

Q. The $120$ permutations of $M A H ES$ are arranged in dictionary order, as if each were an ordinary five-letter word. The last letter of the $8 6^{th}$ word in the list is

$A$

$H$

$S$

$E$