Question

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning, and these words are arranged as in a dictionary. The serial number of the word "GTWENTY" is:

Answer 1

Step 1: Calculate the Number of Words Starting with Each Letter

Words starting with $E$: $6! = 720 / 2 = 360$

Words starting with $G$ and second letter $E$: $5! = 120 / 2 = 60$

Words starting with $G$ and second letter $N$: $5! = 120 / 2 = 60$

Words starting with $GTE$: $4! = 24$

Words starting with $GTN$: $4! = 24$

Words starting with $GTT$: $4! = 24$

Step 2: Add the Serial Position of "GTWENTY"

"GTWENTY" itself contributes $+1$.

Step 3: Total Serial Number of "GTWENTY"

$$360 + 60 + 60 + 24 + 24 + 24 + 1 = 553$$

So, the correct answer is: 553