Question

The rank of the word $SUCCESS$, If all possible permutations of the word $SUCCESS$ are arranged in dictionary order is

• A. $331$
• B. $341$
• C. $351$
• D. $361$

Answer 1

The correct option is A $331$

Alphabets present in the word $SUCCESS$ are $S,U,C,E$
Dictionary order of the alphabet's is $C,E,S,U$
Number of words starting with $C$ $\left(C\_\_\_\_\_\_\right)$ (no two $C$ will be repeated but here we have three $S$) is $\frac{6!}{3!}$

Number of words starting with $E$ $\left(E\_\_\_\_\_\_\right)$ (here we have two $C$ and three $S$) is $\frac{6!}{2!3!}$

Now we want the word stariting with $S$
So, Number of words starting with $SC$ $\left(SC\_\_\_\_\_\right)$ (here we have single $C$ and two $S$) is $\frac{5!}{2!}$

Number of words starting with $SE$ $\left(SE\_\_\_\_\_\right)$ (here we have two $C$ and two $S$) is $\frac{5!}{2!2!}$

Number of words starting with $SS$ $\left(SS\_\_\_\_\_\right)$ (here we have two $C$ and single $S$) is $\frac{5!}{2!}$

Now next word will be $SUCCESS$
Now rank of the word $SUCCESS$ is
$\frac{6!}{3!}+\frac{6!}{2!3!}+\frac{5!}{2!}+\frac{5!}{2!2!}+\frac{5!}{2!}+1$
$\Rightarrow 120+60+60+30+60+1=331$