JEE Main 2024 (Online) 29th January Morning ShiftQuestion 1
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 $\_\_\_\_\_\_$ .
Permutation and Combination
Answer$553$
Solution
Formulas used. (1) Arrangements with one letter twice: $\dfrac{n!}{2!}$(2) Rank = words before + 1Step 1 - Order. E, G, N, T, T, W, Y. Step 2 - First letter E. Rest G, N, T, T, W, Y: $\frac{6!}{2!}=360$. Step 3 - G then E or N. Rest has T, T: $2\cdot\frac{5!}{2!}=120$. Step 4 - GT then E, N or T. Rest of 4 letters all different: $3\cdot4!=72$. Step 5 - GTW. Remaining E, N, T, Y in the order ENTY is the smallest: $0$ before. Step 6 - Rank. $360+120+72+1=553$. Answer: 553