Question

If all the letters of the word ${}^{\prime }RAT{E}^{\prime }$ are arranged in all possible ways and arranged in the dictionary order, then the rank of the word ${}^{\prime }TEA{R}^{\prime }$ is

• A. $20$
• B. $21$
• C. $22$
• D. $23$

Answer 1

Answer: (B)

$21$

We need to find rank of $TEAR$ given letters $A,E,R,T$

Words starting with $A=3!=6$

Words starting with $E=3!=6$

Words starting with $R=3!=6$

Words starting with $TA=2!=2$

Words starting with $TEAR=1$

$\Rightarrow$ Total $=6+6+6+2+1$

$=21$

$\therefore$ Rank is $21.$

Hence, the answer is $21.$