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NDA 1 2024 Maths, question 108

Topic: Probability

Q108

If the letters of the word “TIRUPATI” are written down at random, then what is the probability that both Ts are always consecutive ?

  1. (a) 12\frac{1}{2}
  2. (b) 14\frac{1}{4}Correct answer
  3. (c) 17\frac{1}{7}
  4. (d) 114\frac{1}{14}

Solution.

Answer: (b) 14\frac{1}{4}

  1. TIRUPATI has eight letters with two Ts and two Is.
  2. Total distinct arrangements are 8!/(2!2!).
  3. Treating the adjacent Ts as one block gives 7!/2! arrangements.
  4. Their ratio is 2/8 = 1/4.