recategorized by
425 views
1 votes
1 votes

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. $\text{IAAGN}$
recategorized by

1 Answer

6 votes
6 votes

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.

edited by

Related questions

1 votes
1 votes
2 answers
1
Arjun asked Sep 23, 2019
630 views
Five letters $A, B, C, D$ and $E$ are arranged so that $A$ and $C$ are always adjacent to each other and $B$ and $E$ are never adjacent to each other. The total number of...
2 votes
2 votes
1 answer
2
gatecse asked Sep 18, 2019
713 views
If the letters of the word $\textbf{COMPUTER}$ be arranged in random order, the number of arrangements in which the three vowels $O, U$ and $E$ occur together is$8!$$6!$$...
2 votes
2 votes
1 answer
3
gatecse asked Sep 18, 2019
378 views
If the letters of the word $\text{COMPUTER}$ be arranged in random order, the number of arrangements in which the three vowels $O, U$ and $E$ occur together is$8!$$6!$$3!...
2 votes
2 votes
2 answers
4