Question

If all the letters of the word $"SECRET"$ are arranged in all possible ways and written out in alphabetical(dictionary) order, then the rank of the given word $"SECRET"$ will be

Answer 1

Alphabets present in the word $SECRET$ are $S,E,E,C,R,T,$
Order of the letters according to the alphabet is $C,E,E,R,S,T$

Number of words starting with $C$ $\left(C\_\_\_\_\_\right)$ is $=\frac{5!}{2!}=60$ (as here we have two $E$)

Number of words starting with $E$ $\left(E\_\_\_\_\_\right)$ $=5!=120$ (as here we have single $E$)

Number of words starting with $R$ $\left(R\_\_\_\_\_\right)$ $=\frac{5!}{2!}=60$ (as here we have two $E$)

Number of words starting with $SC$ $\left(SC\_\_\_\_\right)$ $=\frac{4!}{2!}=12$ (as here we have two $E$)

Number of words starting with $SECE$ $\left(SECE\_\_\right)$ $=2!=2$

Next word is $"SECRET"$.
Therefore, rank
$=60+120+60+12+2+1=255$