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  4. 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 :

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Q. 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 :

JEE MainJEE Main 2023Permutations and Combinations

Solution:

Lets arrange the letters of OUGHT in alphabetical order.
G, H, O, T, U
Words starting with
$G ----\rightarrow 4$ !
$H ----\rightarrow 4$ !
$O ----\rightarrow 4$ !
$T G ---\rightarrow 3$ !
$T H ---\longrightarrow 3$ !
$T O G --\rightarrow 2$ !
$T O H --\rightarrow 2$ !
$T O U G H \rightarrow 1$ !
Total $=89$