NCERT · Class 11 · Mathematics · Permutations and CombinationsFind the number of arrangements of the letters of the word 'ALLAHABAD'.
Step-by-Step Solution
The word 'ALLAHABAD' has 9 letters in total, where 'A' repeats 4 times and 'L' repeats 2 times. The number of arrangements is $\frac{9!}{4!2!} = \frac{362880}{24 \times 2} = \frac{362880}{48} = 7560$. Therefore, option B is correct.
Detailed Options Breakdown
Option : 3780
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 1: 7560 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: 15120
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 3: 840
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
💡 Study Guide: This question tests core syllabus concepts from Permutations and Combinations. For formulas, key summaries, and mock exam reference guides, read the full Permutations and Combinations Revision Notes.