Answer: $\mathbf C$
Explanation:
Given word is: $\mathbf {AGAIN}$
After arranging in alphabetical order: $\mathbf {AAGIN}$
No, the number of arrangements are:
Starting with A: AAGIN = 4! = 24 $ ways
Starting with G: GAAIN = $\frac{4!}{2!}= 12$ ways (Since, $\mathrm A$ appears $2$ times)
Starting with I: IAAGN =$ \frac{4!}{2!}$$ = 12 $ ways (Since $\mathrm A$ appears $2$ times)
Now,
Total ways $= 24 + 12 + 12 = 48$ ways.
So, $49^{th}$ word is: $\mathrm {NAAGI}$
and, $50^{th}$ word is: $\mathrm {NAAIG}$
$\therefore \mathbf C$ is the correct option.