All the letters of the word “GTWENTY” are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word “GTWENTY” is _____. [2024]

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Solution

Q.
All the letters of the word “GTWENTY” are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word “GTWENTY” is _____. [2024]

Ans.
(553)

Number of words starts with $E = \frac{6!}{2!}$

Number of words starts with $G E = \frac{5!}{2!}$

Number of words starts with $G N = \frac{5!}{2!}$

Number of words starts with $GTE = 4!$

Number of words starts with $GTN = 4!$

Number of words starts with $GTT = 4!$

Next word will be GTWENTY

$∴$ Rank of GTWENTY $= \frac{6!}{2!} + 2 \times \frac{5!}{2!} + 3 \times 4! + 1 = 553$

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