Question

if the letters of the word ARISE are managed in a row in all possible ways and the arrangements are listed in alphabetical order as in a dictionary,then rank of the word RAISE is?

Answer 1

Answer:

The alphabetical order of the letters of the word RACHIT is: A, C, H, I, R, T. ... Rank of the word RACHIT in dictionary = 4×5! + 1= 4 x 120+1= 481

Answer 2

Answer: 82

Step-by-step explanation:

Given in the question statement that, letters of the word "ARISE" are managed in a row in all possible ways and the arrangements are listed in alphabetical order as in a dictionary.

To Find: The rank of the word Raise among all the possible words, formed from permutation-combination of all the letters of the word ARISE and then placed alphabetically in the dictionary.

Explanation:

• Given word ARISE has 5 letters: A, R, I, S, E.
• Arranging these 5 letters in alphabetical order, we get, A, E, I, R, S
• So, all the words starting with A, E and I will have higher Ranks than RAISE.
• Now, to calculate all the words starting with "A".
• Fixing A at the starting spot, we can get as many as 4! words, i.e.,

       (4 × 3 × 2 × 1) = 24.

• Similarly, Fixing E at the starting spot there will be 4! words again, i.e., 24 words.
• Fixing I at the starting spot, there will be another 4! words, i.e., 24 words
• Now fixing R at the starting spot, all the words with A at the second spot from the left, will have the higher ranks, i.e., 3! words or (3 * 2 * 1) = 6 words.
• Now fixing R at the starting spot, A at the second spot from the left, and then E at the third spot from the left, all the words will have higher Ranks than RAISE since E is alphabetically higher than I. The number of such words will be 2! = 2.
• Finally, fixing R at the starting spot, A at the second spot from the left, and then, I at the third spot from the left, we will get 2 different words, RAIES and RAISE among which, RAIES will have one rank higher than RAISE.
• Therefore, The Rank of the RAISE in the dictionary among all the words obtained from the permutation-combination of the letters of ARISE and arranged alphabetically will be (24 + 24 + 24 + 6 + 2 + 2) = 82

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