Q258 / 270 · NDA 2024 (Phase 1) · Mathematics

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

  • A
    $\frac{1}{2}$
  • Correct answer
    B
    $\frac{1}{4}$
  • C
    $\frac{1}{7}$
  • D
    $\frac{1}{14}$

Solution

Required probability $\begin{aligned} \mathrm{P}(\mathrm{E}) & =\frac{n(\mathrm{E})}{n(\mathrm{~S})}=\frac{2!7!}{8!} \\ & =\frac{2 \times 1 \times 7!}{8 \times 7!}=\frac{1}{4} \end{aligned}$

Hence, the correct answer is option: 'B'.

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