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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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1 Answer

+3 votes

Answer: $\mathbf C$


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)


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.

edited by

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