Question

If all the words that can be formed from the letters of the word ${}^{\prime }GARN{E}^{\prime }$ are arranged in a dictionary order, then the rank of the word ${}^{\prime }RANG{E}^{\prime }$

• A. $101$
• B. $100$
• C. $102$
• D. $78$

Answer 1

Answer: (C)

$102$

Given letters $A,E,G,N,R.$

We need to find rank of $RANGE$

Words starting with $A=4!$

$\Rightarrow$ $E=4!$

$\Rightarrow$ $G=4!$

$\Rightarrow$ $N=4!$

$\Rightarrow$ $RAE=2!$

$\Rightarrow$ $RAG=2!$

$\Rightarrow$ $RANE=1!$

$\Rightarrow$ $RANGE=1$

$\Rightarrow$ Total $=4\times 4!+2\times 2!+1+1=102$

$\therefore$ Rank $=102.$

Hence, the answer is $102.$