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

1.	The letters of the word ‘INDIA’ are arranged as in a dictionary. What are the 1st, 13th, 49th and 60th words?
Answer» 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^thword 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^stword: ADIIN 13^th word: DAIIN 9^th word: NAIID 60^th word: NDIIA

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

Answer»

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^thword 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^stword: ADIIN

13^th word: DAIIN

9^th word: NAIID

60^th word: NDIIA