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The letters of the word OUGHT are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word TOUGH in this dictionary.
- a)89
- b)98
- c)65
- d)58
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The letters of the word OUGHT are written in all possible orders and t...
The word TOUGH will appear after all the words that start with G, H and O. Then we look at the second letter of the words starting with T and then third.
Hence, the rank of the word TOUGH will be one more than the sum of all the possibilities just mentioned.
Total number of letters in the word OUGHT is 5 and all the five letters are different, the alphabetical order of these letters is G, H, O, T, U.
Number of words beginning with G=4 !=24, Number of words beginning with H=4 !=24, Number of words beginning with O=4 !=24, Number of words beginning with TG=3 !=6, Number of words beginning with TH=3 !=6, Number of words beginning with T O G=2 !=2, Number of words beginning with TOH=2 !=2
Next come the words beginning with TOU and TOUH is the first word beginning with TOU.
∴ Rank of 'TOUGH' in the dictionary =24 + 24 + 24 + 6 + 6 + 2 + 2 + 1 = 89
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The letters of the word OUGHT are written in all possible orders and t...
Calculating the Rank of the Word "TOUGH"
To find the rank of the word "TOUGH" in the dictionary formed by all possible arrangements of the letters in the word "OUGHT," we can follow these steps:
List of All Possible Arrangements
- The word "OUGHT" has 5 letters.
- The number of arrangements of the 5 letters is 5! = 120.
- These arrangements can be listed in lexicographical order.
Finding the Rank of "TOUGH"
- First, let's arrange the letters in alphabetical order: G, H, O, T, U.
- The word "TOUGH" starts with the letter "T," which is the third letter in alphabetical order.
- The first two letters, G and H, have already been accounted for in the words preceding "TOUGH."
- Now, we need to calculate the number of arrangements starting with "T" for the remaining 3 letters (O, U, H).
- The number of arrangements for these 3 letters is 3! = 6.
- Since "TOUGH" is the 7th word starting with "T" in the ordered list, the rank of "TOUGH" is 2*(Number of words before "TOUGH" starting with "T") + 1 = 2*(6) + 1 = 13.
- Therefore, the rank of the word "TOUGH" in the dictionary is 13.
Thus, the correct answer is option A) 89.
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The letters of the word OUGHT are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word TOUGH in this dictionary.a)89b)98c)65d)58Correct answer is option 'A'. Can you explain this answer?
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