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Consider all possible words obtained by arranging all the letters of the word $\textbf{AGAIN}$. These words are now arranged in the alphabetical order,  as in a dictionary. The fiftieth word in this arrangement is

1. $\text{IAANG}$
2. $\text{NAAGI}$
3. $\text{NAAIG}$
4. $\text{IAAGN}$

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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.

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