The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series

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

Smart Achievers · Accepted Answer

(1)

We arrange the letters of OUGHT in alphabetical order as G,H,O,T,U

In dictionary words starting with

$G \cdot \cdot \cdot \cdot \cdot \cdot \cdot \to 4!$

$H \cdot \cdot \cdot \cdot \cdot \cdot \cdot \to 4!$

$O \cdot \cdot \cdot \cdot \cdot \cdot \cdot \to 4!$

$T G \cdot \cdot \cdot \cdot \cdot \cdot \to 3!$

$T H \cdot \cdot \cdot \cdot \cdot \cdot \to 3!$

$T O G \cdot \cdot \cdot \cdot \cdot \to 2!$

$T O H \cdot \cdot \cdot \cdot \cdot \to 2!$

$\frac{T O U G H \to 1!}{Total=89}$

Solution

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

1 89

2 100

3 258

4 237

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