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

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

NTA AbhyasNTA Abhyas 2022

Solution:

R A M A Y A N
$\begin{array}{lllllll}4 & 1 & 2 & 1 & 5 & 1 & 3 \\ 5 & 0 & 2 & 0 & 2 & 0 & 0\end{array}$
$\begin{array}{lllllll}2 & 0 & 2 & 0 & 2 & 0 & 0\end{array}$
$\frac{6 !}{3 !} \frac{5 !}{3 !} \frac{4 !}{2 !} \frac{3 !}{2 !} 2 ! 1 ! 0$ !
Rank of RAMAYAN
$=5\times \frac{6 !}{3 !}+2\times \frac{4 !}{2 !}+2\times 2!+1$
$=629$