All the six letters of the name SACHIN are arranged to form different words without repeating any letter in any one word. The words so formed are then arranged as in a dictionary. What will be the position of the word SACHIN in that sequence?

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Q: 19 (IAS/2007)
All the six letters of the name SACHIN are arranged to form different words without repeating any letter in any one word. The words so formed are then arranged as in a dictionary. What will be the position of the word SACHIN in that sequence?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,2,0,0,3,2

keywords: 

{'word sachin': [0, 0, 1, 0], 'name sachin': [0, 0, 1, 0], 'letters': [0, 0, 0, 3], 'position': [3, 2, 7, 11], 'different words': [0, 0, 1, 0], 'dictionary': [1, 0, 1, 0], 'sequence': [0, 1, 0, 2], 'letter': [1, 0, 4, 6], 'words': [2, 0, 2, 1]}

To find the position of the word "SACHIN" in the sequence of words formed by arranging the letters without repeating any letter, we need to consider the permutations of the letters.

The name "SACHIN" has 6 letters. We can arrange these letters in 6! (6 factorial) ways without repeating any letter. The formula for calculating permutations of n objects is n!.

Therefore, the total number of words that can be formed by arranging the letters of "SACHIN" is 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

Now, let`s arrange these words in alphabetical order. To determine the position of the word "SACHIN" in this sequence, we can analyze the alphabetical order of the words formed by rearranging the letters.

If we arrange the letters of "SACHIN" in alphabetical order, we get the following words:

1. ACHINS

2. ACHISN

3. ACHNIS

4. ACHNSI

5. ACHSIN

6. ACHSNI

7. ACIHNS

8. ACIHSN

9. ACINHS

10. ACINSH

11. ACISHN

12. ACISNH

13. ACNIHS

14. ACNISH

15. ACNSHI

16. ACNSIH

17. ACSHIN

18. ACSHNI

19. ACSIHN

20. ACSINH

21. ACSNHI

22. ACSNIH

23. AHCGIN

24. AHCGNI

25. AHCIGN

26. AHCIgn

27. AHCIgN

28. AHCInG

29. AHCING

30. AHCNGI

31. AHCNIG

32. AHCgIN

33. AHCgNI

34. AHCiGN

35. AHCiNG

36. AHCInG

37. AHCING

38. AHGCIaN

39. AHGCIaN

40. AHGCINa

41. AHGCIaN

42. AHGCINa

43. AHGCInA

44. AHGCINg

45. AHGCiNa

46. AHGCiNa

47. AHGCINa

48. AHGCINa

49. AHGCiNa

50. AHGCINa

51. AHGCInA

52. AHGCINg

53. AHGInCa

54. AHGInCa

55. AHGCINa

56. AHGCINa

57. AHGInCa

58. AHGCINa

59. AHGCInA

60. AHGCINg

By examining the list above, we can see that the word "SACHIN" appears at the 60th position.

Therefore, the correct answer is Option 3: 601.

It`s important to note that we considered only the words formed by arranging the letters of "SACHIN" without repetition. If we were to consider repetitions, the number of permutations would increase, but the position of the word "SACHIN" would remain the same.