Multiple choice

The letters of the word $\text{ALLAHABAD}$ are arranged at random. The probability that in the word so formed, all similar letters are found together, is

  1. $\dfrac{1}{63}$
  2. $\dfrac{16}{17}$
  3. $\dfrac{51}{9!}$
  4. $\dfrac{1}{81}$
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A Correct answer
AI explanation

The total number of arrangements for the 9 letters in ALLAHABAD is 9! / (4! * 2!) = 7560. For all similar letters to be together, the 4 As, 2 Ls, and the remaining distinct letters (H, B, D) are treated as 5 single units. These 5 units can be arranged among themselves in 5! = 120 ways. The probability is therefore 120 / 7560, which simplifies to 1/63.

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