Question

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

Answer 1

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

⇒ 1^st word: ADIIN 

To find other words: 

Case 1: words starting with A 

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

⇒ 13^th word starts with D and is DAIIN

Case 2: words starting with D

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

Case 3: Words starting with I

Number of words = 4! = 24

⇒ (12+12+24+1)^th = 49^th word starts with N and is NAIID

Case 4: Words starting with N

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

⇒ (48+12)^th word is the last word which starts with N 

⇒ 60^th word = NDIIA 

1^st word: ADIIN 

13^th word: DAIIN 

9^th word: NAIID

60^th word: NDIIA