Permutations and Combinations

We have, E, E, L, R, T, T
Words starting with E,L,R, where first letter is T
(i) Starting with E:‌

5!

2!

=60
(ii) Starting with L:‌

5!

2!2!

=30
(iii) Starting with R:‌

5!

2!2!

=30
Total =60+30+30=120
Fixed TE next is T
Letters before T is E,L,R
Each gives 3!=6
⇒3×6=18
Now, fixed TETL, next is E one word before TETLE
k is remaining letter which is before 2 letters.
Final letter is TETLER =1
‌ Rank ‌=120+18+2+1=141.