JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Permutations and Combinations

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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 :

(A)89✓ Correct
(B)84
(C)86
(D)79

Answer: (A)

Solution

Arranged alphabetically the letters are

G, H, O, T, U

. The words beginning with

G

H

O

number

3 \times 4! = 72

. Among the words beginning with

T

, those with second letter

G

H

number

2 \times 3! = 12

; those beginning

T O G

T O H

number

2 \times 2! = 4

; and

T O U G H

is the very first word beginning with

T O U

. Counting up to and including

T O U G H

, the serial number is

72 + 12 + 4 + 1 = 89

JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Single correct option

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