Question

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is

(1) 89 

(2) 84 

(3) 86 

(4) 79

Answer 1

Correct option is (1) 89 

Let arrange the letters of OUGHT in alphabetical order.

G, H, O, T, U

Words starting with

Answer 2

An interesting problem that involves some permutations

First, the "dictionary order" of the letters of the word "OUGHT" is G, then H, then O, then T, then U.  Then, the number of ways to arrange (permutation of five things taken five at a time) five letters is 24. So ... all of the G permutation come first, then all of the H permutations, followed by all of the O permutations.  So there are 72 entries already before any "words" that begin with T.  Following along in this same way, there are 6 TG words, and then 6 TH words, which brings us to 84 entries.  Next we have 2 TOG words, and 2 TOH words, which brings us to 88 entries.  Finally we are at TOU and in dictionary order the next word would be TOUGH.  Therefore, the answer is 89; the serial order of the word TOUGH would be 89th in the dictionary.