Permutations & Combinations
Dictionary rank of a word
nta_pyq_2023_jan
Grade 11

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:
89
84
86
79

Step-by-Step Solution

Key Concept: Arrange letters alphabetically, count words that come before TOUGH lexicographically.
Alphabetical order: G,H,O,T,U. Words starting with G:4!=24, H:4!=24, O:4!=24; TG---:3!=6, TH--:3!=6; TOG-:2!=2, TOH-:2!=2; TOUG:1!=1. Total before TOUGH = 24+24+24+6+6+2+2 = 88. TOUGH is 89th.
Correct Answer: 1

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