JEE MAIN - Mathematics (2023 - 29th January Evening Shift - No. 3)
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 :
79
84
89
86
Explanation
Lets arrange the letters of OUGHT in alphabetical
order.
G, H, O, T, U
Words starting with
$$ \begin{aligned} & \mathrm{G}----\rightarrow 4 ! \\\\ & \mathrm{H}----\rightarrow 4 ! \\\\ & \mathrm{O}----\rightarrow 4 ! \end{aligned} $$
$\mathrm{T} \,\mathrm{G}---\rightarrow 3$ !
T H $---\rightarrow 3$ !
T O $\mathrm{G}--\rightarrow 2$ !
T O H $--\rightarrow 2$ !
T O U G H $\rightarrow 1$ !
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Total = 89
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