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If letters of the word R E G U L A T I O N S are randomly arranged, then the probability that there are exactly four letters between R and S is

Options

  1. A6 55
  2. B3 55
  3. C5 11
  4. D6 11

Correct answer

A. 6 55

Step-by-step solution

Total cases = 11 ! Number of favourable cases = 2 ! × 9 C 4 × 4 ! × 6 ! Hence, required probability = 2 ! × 9 C 4 × 4 ! × 6 ! 11 ! = 2 ! × 9 ! × 4 ! × 6 ! 11 ! × 5 ! × 4 ! = 2 × 6 11 × 10 = 6 55

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