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