The letters of the word 'MASTER ' are permutated in all possible ways and the words thus formed arranged as in dictionary. Find rank of word (i) REMAST  (ii) MASTER  (iii) EAMCET

Alphabetical order of the word MASTER is A,E,M,R,S,T
(i) REMAST
No. of 6 latter word starting with A ..........=5!
No. of 6 latter word starting with E ..........=5!
No. of 6 latter word starting with M ..........=5!
No. of 6 latter word starting with R A ..........=4!
No. of 6 latter word starting with R E A ..........=3!
No. of 6 latter word starting with REMAST ..........=1
Rank of REMAST=3(5!)+4!+3!+1=391
(ii) MASTER
Alphabetical order is AEMRST
No.of 6 latte word starting with A ............=5!
No.of 6 latte word starting with E ............=5!
No.of 6 latte word starting with MAE ............=3!
No.of 6 latte word starting with  MAR ............=3!
No.of 6 latte word starting with MASE ............=2!
No.of 6 latte word starting with MASR ............=2!
Rank of MASTER =2(5!)+2(3!)+2(2!)+1=257

(iii) EAMCET
Alphabetical order is A,C,E,E,M,T
No.of 6 latte word starting with A = $\frac{5!}{2!}$
No.of 6 latte word starting with C= $\frac{5!}{2!}$
No.of 6 latte word starting with EAC =3!
No.of 6 latte word starting with EAE =3!
No.of 6 latte word starting with EAMCET =1
RANK=$2\left(\frac{5!}{2!}\right)+3!+3!+1=133$