The Gateway to Computer Science Excellence
0 votes
15 views

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. $\text{IAAGN}$
in Combinatory by Veteran (424k points)
recategorized by | 15 views

1 Answer

0 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.

by Boss (12.9k points)
edited by

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,648 questions
56,429 answers
195,205 comments
99,907 users