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All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"?
  • a)
    70
  • b)
    74
  • c)
    64
  • d)
    60
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
All the rearrangements of the word "DEMAND" are written without inclu...
To find the rank of the word "DEMAND" among all possible rearrangements without any two D's appearing together, we can follow the steps below:

1. Identify the total number of arrangements:
- The word "DEMAND" has 6 letters, but since it contains 2 identical D's, we have to divide the total number of arrangements by 2.
- So, the total number of arrangements = 6!/2! = 6*5*4*3*2*1 / 2*1 = 720/2 = 360.

2. Arrange the letters in alphabetical order:
- The letters in "DEMAND" are A, D, D, E, M, N.
- To find the rank of "DEMAND," we need to arrange these letters in alphabetical order.
- The alphabetical order is: A, D, D, E, M, N.

3. Determine the rank:
- To find the rank, we will consider the letters one by one.
- The first letter is "A". There are no letters before "A" in alphabetical order, so it does not affect the rank.

- The second letter is "D". Since there is one "D" before it, we need to consider all the arrangements starting with "D" as the first letter.
- The remaining letters are D, E, M, and N.
- Among these, the alphabetical order is: D, E, M, N.
- The total number of arrangements = 4!/2! = 4*3*2*1 / 2*1 = 24/2 = 12.
- So, there are 12 arrangements starting with "D" as the first letter.

- The third letter is also "D". Since there is one more "D" before it, we need to consider all the arrangements starting with "D" as the first two letters.
- The remaining letters are E, M, and N.
- Among these, the alphabetical order is: D, E, M, N.
- The total number of arrangements = 3! = 3*2*1 = 6.
- So, there are 6 arrangements starting with "D" as the first two letters.

- The fourth letter is "E". Since there are two "D"s before it, it does not affect the rank.

- The fifth letter is "M". Since there are two "D"s before it, it does not affect the rank.

- The sixth letter is "N". Since there are two "D"s before it, it does not affect the rank.

4. Calculate the rank:
- The rank of "DEMAND" = 12 + 6 = 18.

Therefore, the rank of the word "DEMAND" among all possible rearrangements without any two D's appearing together is 18.
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Community Answer
All the rearrangements of the word "DEMAND" are written without inclu...
Number of rearrangements of word DEMAND = 6!/2! = 360
Number of rearrangements of word DEMAND where 2 D’s appear together = 5! = 120
Number of rearrangements of word DEMAND where 2D’s do not appear together =
360 – 120 = 240
Words starting with ‘A’; without two D’s adjacent to each other
Words starting with A: 5!2! = 60
Words starting with A where 2 D’s are together = 4! = 24
Words starting with ‘A’, without two D’s adjacent to each other = 36
Next we have words starting with D.
Within this, we have words starting with DA: 4! words = 24 words
Then words starting with DE
Within this, words starting with DEA ⇒ 3! = 6 words
Then starting with DED – 3! = 6 words
Then starting with DEM
⇒ First word is DEMADN
⇒ Second is DEMAND
Rank of DEMAND = 36 + 24 + 6 + 6 + 2 = 74
Hence, the correct option is (b).
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All the rearrangements of the word "DEMAND" are written without including any word that has two D's appearing together. If these are arranged alphabetically, what would be the rank of "DEMAND"?a)70b)74c)64d)60Correct answer is option 'B'. Can you explain this answer?
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