Question:
If all the letters of the word MESSI are permuted in all possible ways and the words [with or without meaning] thus formed are arranged in dictionary order, then the rank of the word MESSI is
If all the letters of the word MESSI are permuted in all possible ways and the words [with or without meaning] thus formed are arranged in dictionary order, then the rank of the word MESSI is
Show Hint
Always divide by the factorial of the repetition count (\( 2! \) for the two 'S' letters) when calculating permutations of remaining items. Forgetting this division is the most common reason for getting an inflated rank.
Updated On: Jun 7, 2026
- \( 18 \)
- \( 27 \)
- \( 23 \)
- \( 26 \)
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The Correct Option is D
Solution and Explanation
Concept:
To find the dictionary rank of the word **MESSI**, we first arrange its constituent letters in alphabetical ascending order:
E, I, M, S, S
We then systematically calculate how many words can be formed starting with letters that appear before 'M'.
Step 1: Counting words starting with letters before 'M'.
• Words starting with **E**: The remaining letters are I, M, S, S (where S repeats twice). \[ \text{Number of words} = \frac{4!}{2!} = \frac{24}{2} = 12 \]
• Words starting with **I**: The remaining letters are E, M, S, S (where S repeats twice). \[ \text{Number of words} = \frac{4!}{2!} = \frac{24}{2} = 12 \]
Total words formed before any word starting with M \( = 12 + 12 = 24 \).
Step 2: Alphabetical tracking for words starting with 'M'.
The next words will begin with **M**. Following alphabetical order for the remaining letters (E, I, S, S):
• The first available word starting with **ME** will arrange the remaining letters (I, S, S) alphabetically: \[ \text{Next word (25th): } \textbf{M E I S S} \]
• The very next word in alphabetical sequence swaps the position of 'I' with the next available letter 'S': \[ \text{Next word (26th): } \textbf{M E S S I} \]
Thus, **MESSI** is exactly the 26th word in the list.
Step 1: Counting words starting with letters before 'M'.
• Words starting with **E**: The remaining letters are I, M, S, S (where S repeats twice). \[ \text{Number of words} = \frac{4!}{2!} = \frac{24}{2} = 12 \]
• Words starting with **I**: The remaining letters are E, M, S, S (where S repeats twice). \[ \text{Number of words} = \frac{4!}{2!} = \frac{24}{2} = 12 \]
Total words formed before any word starting with M \( = 12 + 12 = 24 \).
Step 2: Alphabetical tracking for words starting with 'M'.
The next words will begin with **M**. Following alphabetical order for the remaining letters (E, I, S, S):
• The first available word starting with **ME** will arrange the remaining letters (I, S, S) alphabetically: \[ \text{Next word (25th): } \textbf{M E I S S} \]
• The very next word in alphabetical sequence swaps the position of 'I' with the next available letter 'S': \[ \text{Next word (26th): } \textbf{M E S S I} \]
Thus, **MESSI** is exactly the 26th word in the list.
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