Question

If the words formed by using the letter of the word $AGAIN$ are arranged in the form of dictionary the $50th$ word is:

• A. $NAAGI$
• B. $NAAIG$
• C. $NAGAI$
• D. $NAIAG$

Answer 1

The correct option is B $NAAIG$

Let us consider the characters in ascending order is $(A,G,I,N)$

Let us consider the number of words starting with $A=4!=24$

Let us consider the number of words starting with $G=\frac{4!}{2!}=12$

Let us consider the number of words starting with $I=\frac{4!}{2!}=12$

therefore,

The total number until now $=48$

Hence, $NAAGI$ is ${49}^{th}$ word and $NAAIG$ is ${50}^{th}$ word.