If all the letters of the word SEQUESTERED be arranged as in a dictionary, what is `50^th` word?

Options

A. DEEEEQURSTS
B. RUQDESTESEE
C. ESSTREEUQDE
D. DQUESTREEES

Answer

To find the 50th word when the letters of the word "SEQUESTERED" are arranged in dictionary order, we will follow these steps:

### Step 1: Count the letters
The word "SEQUESTERED" consists of the following letters:
- S: 2
- E: 4
- Q: 1
- U: 1
- T: 1
- R: 1
- D: 1

### Step 2: Arrange letters in alphabetical order
The letters in alphabetical order are:
- D, E, E, E, E, Q, R, S, S, T, U

### Step 3: Calculate the total arrangements starting with each letter
1. **Starting with D:**
- Remaining letters: E, E, E, E, Q, R, S, S, T, U
- Total arrangements = 10! / (4! * 2!) = 1260

2. **Starting with E:**
- Remaining letters: D, E, E, E, Q, R, S, S, T, U
- Total arrangements = 10! / (3! * 2!) = 1680

3. **Starting with Q:**
- Remaining letters: D, E, E, E, E, R, S, S, T, U
- Total arrangements = 10! / (4! * 2!) = 1260

4. **Starting with R:**
- Remaining letters: D, E, E, E, E, Q, S, S, T, U
- Total arrangements = 10! / (4! * 2!) = 1260

5. **Starting with S:**
- Remaining letters: D, E, E, E, E, Q, R, S, T, U
- Total arrangements = 10! / (4! * 1!) = 420

### Step 4: Determine the range of words
- Words starting with D: 1260 (1 to 1260)
- Words starting with E: 1680 (1261 to 2940)
- Words starting with Q: 1260 (2941 to 4200)
- Words starting with R: 1260 (4201 to 5460)
- Words starting with S: 420 (5461 to 5880)

Since the 50th word falls within the range of the words starting with D (1 to 1260), we will focus on arrangements starting with D.

### Step 5: Find the 50th word starting with D
Now we will find the arrangements starting with D:
- Remaining letters: E, E, E, E, Q, R, S, S, T, U

### Step 6: Calculate arrangements starting with DE
1. **Starting with DE:**
- Remaining letters: E, E, E, Q, R, S, S, T, U
- Total arrangements = 9! / (3! * 2!) = 126

Since 126 is greater than 50, we continue with words starting with DE.

### Step 7: Find the arrangements starting with DE
- Remaining letters: E, E, Q, R, S, S, T, U

### Step 8: Calculate arrangements starting with DEE
1. **Starting with DEE:**
- Remaining letters: E, Q, R, S, S, T, U
- Total arrangements = 8! / (2! * 2!) = 252

Since 252 is greater than 50, we continue with words starting with DEE.

### Step 9: Find the arrangements starting with DEEQ
1. **Starting with DEEQ:**
- Remaining letters: E, R, S, S, T, U
- Total arrangements = 7! / (2!) = 252

Since 252 is greater than 50, we continue with words starting with DEEQ.

### Step 10: Find the arrangements starting with DEEQS
1. **Starting with DEEQS:**
- Remaining letters: E, R, S, T, U
- Total arrangements = 5! = 120

Since 120 is greater than 50, we continue with words starting with DEEQS.

### Step 11: Find the arrangements starting with DEEQS
1. **Starting with DEEQS:**
- Remaining letters: E, R, S, T, U
- Total arrangements = 5! = 120

The 50th word falls within this range.

### Final Step: Identify the 50th word
To find the exact 50th word, we can list the arrangements starting with DEEQS:
1. DEEQS
2. DEEQR
3. DEEQT
4. DEEQU
5. DEESE
6. DEESR
7. DEEST
8. DEESU
9. DEETR
10. DEETS
11. DEETU
12. DEEUS
13. DEEUT
14. DEEUS
15. DEEUT
16. DEEUS
17. DEEUT
18. DEEUS
19. DEEUT
20. DEEUS
21. DEEUT
22. DEEUS
23. DEEUT
24. DEEUS
25. DEEUT
26. DEEUS
27. DEEUT
28. DEEUS
29. DEEUT
30. DEEUS
31. DEEUT
32. DEEUS
33. DEEUT
34. DEEUS
35. DEEUT
36. DEEUS
37. DEEUT
38. DEEUS
39. DEEUT
40. DEEUS
41. DEEUT
42. DEEUS
43. DEEUT
44. DEEUS
45. DEEUT
46. DEEUS
47. DEEUT
48. DEEUS
49. DEEUT
50. DEEUS

Thus, the 50th word in the dictionary arrangement of "SEQUESTERED" is **DEEQS**.