The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?

LohaHridoy
  1. 242
  2. 240
  3. 251
  4. 275

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Answer: Option 1

The order of each letter in the dictionary is ABLORU. Now, with A in the beginning, the remaining letters can be permuted in 5! ways. Similarly, with B in the beginning, the remaining letters can be permuted in 5! ways. With L in the beginning, the first word will be LABORU, the second will be LABOUR. Hence, the rank of the word LABOUR is, 5! + 5! + 2 = 120 + 120 + 2 = 242 Note: 5! = 5 × 4 × 3 × 2 × 1 = 120

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