# DBT JRF 2022 — Question 17

Exam: DBT JRF 2022 · Section: A · Topic: Aptitude › Permutations & Combinations · Difficulty: Medium

## Question

How many words can be formed with the letters of the word 'PATALIPUTRA'?

## Options

- **A.** $\frac{11!}{2! \  3!}$
- **B.** $\frac{11!}{2! \  2! \  3!}$
- **C.** $\frac{11!}{3! \ 1! \  2!}$
- **D.** $\frac{11!}{3!}$

## Answer

Option B

## Explanation

Permutations with repeated letters — word PATALIPUTRA: The word PATALIPUTRA has 11 letters. Count each letter's frequency: P–2, A–3, T–2, L–1, I–1, U–1, R–1 (Total = 2+3+2+1+1+1+1 = 11 ✔) Formula for arrangements with repeated elements: $\text{Number of words} = \frac{n!}{n_1! \cdot n_2! \cdot n_3! \cdots} = \frac{11!}{2! \times 3! \times 2!}$ where 2! accounts for P×2, 3! for A×3, and 2! for T×2. Answer: $\dfrac{11!}{2! \times 2! \times 3!}$ (Option 2).

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