If Letters A,A,A,M,N,R,Y are arranged in dictionary order then the word whose rank is 629th is :-

Question

If Letters A,A,A,M,N,R,Y are arranged in dictionary order then the word whose rank is 629th is :- (A) RAMAYAN (B) RAMAYNA (C) RAMYANA (D) RMAAYNA

Tardigrade Admin · Accepted Answer

R A M A Y A N beginarraylllllll4 1 2 1 5 1 3 5 0 2 0 2 0 0 endarray beginarraylllllll2 0 2 0 2 0 0 endarray (6 !/3 !) (5 !/3 !) (4 !/2 !) (3 !/2 !) 2 ! 1 ! 0 ! Rank of RAMAYAN =5× (6 !/3 !)+2× (4 !/2 !)+2× 2!+1 =629

Q. If Letters A,A,A,M,N,R,Y are arranged in dictionary order then the word whose rank is $62 9^{t h}$ is :-

RAMAYAN

RAMAYNA

RAMYANA

RMAAYNA

R A M A Y A N
$45102210521030$
$2020200$
$\frac{6 !}{3 !} \frac{5 !}{3 !} \frac{4 !}{2 !} \frac{3 !}{2 !} 2! 1! 0$ !
Rank of RAMAYAN
$= 5 \times \frac{6 !}{3 !} + 2 \times \frac{4 !}{2 !} + 2 \times 2! + 1$
$= 629$

Q. If Letters A,A,A,M,N,R,Y are arranged in dictionary order then the word whose rank is 629th is :-