Question

Different words are being formed by arranging the letters of the word ARRANGE. All the words obtained are written in the form of a dictionary

The rank of the word ARRANGE in a dictionary is

• A. 344
• B. 342
• C. 343
• D. 340

Answer 1

Answer: (B)

342

Starting with AA: Letters are E G N R R: $\frac{5!}{2!}=60$

Starting with AE: Letters are A G N R R: $\frac{5!}{2!}=60$

Starting with AG: Letters are A E N R R: $\frac{5!}{2!}=60$

Starting with AN: Letters are A E G R R: $\frac{5!}{2!}=60$

Starting with ARA: Letters are E G N R: $4!=24$

Starting with ARE: Letters are A G N R: $4!=24$

Starting with ARG: Letters are A E N R: $4!=24$

Starting with ARN: Letters are A E G R: $4!=24$

Starting with ARRAE: Letters are G N: $2!=2$

Starting with ARRAG: Letters are E N: $2!=2$

Starting with ARRANE: Letter is G: $1!=1$

Finally, we get ARRANGE $\Rightarrow 1$ word

Thus, its rank = $60\times 4+24\times 4+2\times 2+1+1=342$