How many words can be formed with the letters of the word ‘PATALIPUTRA’?
A. 11!/2! 3!
B. 11!/2! 2! 3!
C. 11/3!1! 21
D. 11!/3!

Forming Words from ‘PATALIPUTRA’: A Permutation Puzzle

Introduction

Permutation puzzles like these are popular in competitive exams and logical reasoning tests. One such classic question is:

How many distinct words can be formed using all the letters of the word ‘PATALIPUTRA’?

Let’s break it down step-by-step and find the correct answer.

Step 1: Count the Total Letters

The word PATALIPUTRA has 11 letters.

Step 2: Identify Repeating Letters

Let’s look at the repetition of letters:

• A appears 3 times
• T appears 2 times
• P appears 2 times
• The other letters (L, I, U, R) appear once each

Step 3: Use the Permutation Formula

The general formula for finding permutations when letters repeat is:

  The formula is:         (n!) / (p₁! × p₂! × … × pₖ!)

Where:

• n!  is the factorial of the total number of letters
• p1!,p2!,… are the factorials of each repeated letter count

So in our case:

                                                11!/ 3!⋅2!⋅2!

Final Answer:

✅ Correct Option: B.     11!/ 2!⋅2!⋅3!

This accounts for all repeating letters and gives us the total number of unique arrangements.

Why It Matters

This type of question helps build your understanding of:

• Factorials and permutations
• Managing repetitions in combinatorics
• Real-world applications in data science, linguistics, and cryptography

Conclusion

The number of distinct words that can be formed from ‘PATALIPUTRA’ is calculated using the formula:

                                     11!/ 2!⋅2!⋅3!

This accounts for repeating letters A, T, and P, giving us the precise number of permutations possible.

Always remember to count your repeated letters carefully—it’s the key to solving such problems accurately!