Question

The letters of the word TOUGH are written in all possible orders and the words are written out as in a dictionary. Then the rank of the word TOUGH is:

• A. 120
• B. 88
• C. 89
• D. 90

Hint:

Lexicographic rank uses permutations systematically.

Answer 1

The Correct Option is C

Letters in alphabetical order: G, H, O, T, U Words before TOUGH: - Starting with G: 4! = 24 - Starting with H: 4! = 24 - Starting with O: 4! = 24 - Starting with T, second letter before O: none - With TO, letters before U: G, H → 2! = 2 Total before TOUGH: 24+24+24+16=88 Rank = 88+1 = 89