Podcast
Questions and Answers
What is the primary difference in calculating the rank of a word with unique letters versus a word with repeating letters?
What is the primary difference in calculating the rank of a word with unique letters versus a word with repeating letters?
- Unique letter words require assigning alphabetical order from right to left, while repeating letter words assign from left to right.
- Repeating letter words require dividing each factorial term by the factorial of the count of repeating letters, while unique letter words do not. (correct)
- Repeating letter words use a different base for factorial calculation compared to unique letter words.
- Unique letter words involve listing numbers to the left that are smaller, while repeating letter words list numbers to the right.
In the method described, what is the significance of numbering the letters of a word according to their alphabetical order?
In the method described, what is the significance of numbering the letters of a word according to their alphabetical order?
- It determines the visual appeal of the word in a dictionary.
- It is solely for categorizing words based on their first letter.
- It simplifies the multiplication step in the rank calculation.
- It establishes a basis for counting smaller numbers to the right, reflecting the lexicographical order. (correct)
When calculating the rank of 'TRILOK,' what does the '5' in the term '(5 * 5!)' represent?
When calculating the rank of 'TRILOK,' what does the '5' in the term '(5 * 5!)' represent?
- The number of letters to the right of 'T' in 'TRILOK' that are smaller than 'T' alphabetically. (correct)
- The total number of letters in the word 'TRILOK'.
- The alphabetical position of the letter 'T' in the English alphabet.
- The factorial value assigned to the position of 'T' in the word.
In the 'ANURADHA' example, why is it necessary to divide by the factorial of the count of repeating letters?
In the 'ANURADHA' example, why is it necessary to divide by the factorial of the count of repeating letters?
If a word has the letter 'E' repeated three times, what value would you divide the corresponding factorial term by during rank calculation?
If a word has the letter 'E' repeated three times, what value would you divide the corresponding factorial term by during rank calculation?
What is the purpose of adding '1' at the end of the calculation for the rank of a word?
What is the purpose of adding '1' at the end of the calculation for the rank of a word?
Consider the word 'HELLO'. After numbering the letters alphabetically, which sequence of numbers smaller to the right would you obtain?
Consider the word 'HELLO'. After numbering the letters alphabetically, which sequence of numbers smaller to the right would you obtain?
For the word 'APPLE', what factorial term would be used when considering the first 'P' from the left during rank calculation?
For the word 'APPLE', what factorial term would be used when considering the first 'P' from the left during rank calculation?
What is the primary advantage of using the short tricks to find the rank of words, as opposed to listing all possible permutations?
What is the primary advantage of using the short tricks to find the rank of words, as opposed to listing all possible permutations?
If 'VINEET' has alphabetical order E=1, I=2, N=3, T=4, V=5, what numbers smaller to the right of the first 'E' need to be considered to compute the rank?
If 'VINEET' has alphabetical order E=1, I=2, N=3, T=4, V=5, what numbers smaller to the right of the first 'E' need to be considered to compute the rank?
Flashcards
Word Rank
Word Rank
Arranging words in dictionary order and determining a word's position.
Unique Letter Words
Unique Letter Words
Words with no letters repeating.
Repeating Letter Words
Repeating Letter Words
Words containing one or more letters that appear multiple times.
Ranking a Unique Word
Ranking a Unique Word
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Ranking a Repeating Word
Ranking a Repeating Word
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Rank of 'TRILOK'
Rank of 'TRILOK'
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Rank of 'ANURADHA'
Rank of 'ANURADHA'
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Study Notes
Finding the Rank of a Word Using Short Tricks
- The lecture focuses on finding the rank of words in a dictionary order using short tricks, which saves time compared to standard methods.
- The concept is that if its alphabets were set according to the dictionary, that particular word will come as what number.
- These type of question are often asked in exams.
- Two types of words exist: those with unique letters and those with repeated letters.
- Two example questions will be explained and a third question has been set as homework.
Rank of a Word with Unique Letters: "TRILOK"
- Write the word as is.
- Number the word's letters according to their alphabetical order.
- I = 1, K = 2, L = 3, O = 4, R = 5, T = 6
- List how many numbers to the right are smaller than the current number.
- T(6): 5, R(5): 4, I(1): 0, L(3): 1, O(4): 1, K(2): 0
- Assign factorial values starting from 0! from right to left.
- K: 0!, O: 1!, L: 2!, I: 3!, R: 4!, T: 5!
- Multiply the corresponding numbers and factorials, then add 1.
- Calculation: (5 * 5!) + (4 * 4!) + (0 * 3!) + (1 * 2!) + (1 * 1!) + (0 * 0!) + 1
- Rank of "TRILOK" = 600 + 96 + 0 + 2 + 1 + 0 + 1 = 700
Rank of a Word with Repeating Letters: "ANURADHA"
- Write the word as is.
- Number the word's letters according to their alphabetical order, considering repetitions.
- A = 1, D = 2, H = 3, N = 4, R = 5, U = 6
- The letters "A" is repeated.
- Numbering: A(1), N(4), U(6), R(5), A(1), D(2), H(3), A(1)
- List how many numbers to the right are smaller than the current number.
- A(1): 0, N(4): 4, U(6): 5, R(5): 4, A(1): 0, D(2): 1, H(3): 1, A(1): 0
- Assign factorial values starting from 0! from right to left.
- A: 0!, H: 1!, D: 2!, A: 3!, R: 4!, U: 5!, N: 6!, A: 7!
- Divide each factorial term by the factorial of the count of repeating letters to the right, including itself.
- A: 3!, N: 2!, U: 2!, R: 2!, A: 2!, D: 1!, H:1!, A: 1!
- After that multiply and add one to arrive at the final answer.
- Calculation: (0 * 7!/3!) + (4 * 6!/2!) + (5 * 5!/2!) + (4 * 4!/2!) + (0 * 3!/2!) + (1 * 2!/1!) + (1 * 1!/1!) + (0 * 0!/1!) + 1
Homework
- Find the rank of the word, "VINEET".
- Comment your answer in the comment section.
- The correct answer will be pinned.
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