# The letters of the word ‘INDIA’ are arranged as in a dictionary.

Question:

The letters of the word ‘INDIA’ are arranged as in a dictionary. What are the $1^{\text {st }}, 13^{\text {th }}, 49^{\text {th }}$ and $60^{\text {th }}$ words?

Solution:

Alphabetical arrangement of letters: A,D,I,N

$\Rightarrow 1^{\text {st }}$ word: ADIIN

To find other words:

Case 1: words starting with A

Number of words $=\frac{4 !}{2 !}=12$

$\Rightarrow 13^{\text {th }}$ word starts with D and is DAllN

Case 2: words starting with D

Number of words $=\frac{4 !}{2 !}=12$

Case 3: Words starting with I

Number of words $=4 !=24$

$\Rightarrow(12+12+24+1)^{\text {th }}=49^{\text {th }}$ word starts with $\mathrm{N}$ and is $\mathrm{NAllD}$

Case 4: Words starting with N

Number of words $=\frac{4 !}{2 !}=12$

$\Rightarrow(48+12)^{\text {th }}$ word is the last word which starts with $\mathrm{N}$

$\Rightarrow 60^{\text {th }}$ word $=$ NDIIA

$13^{\text {th }}$ word: DAllN
$9^{\text {th }}$ word: NAllD
$60^{\text {th }}$ word: NDIIA