MHT CET · Maths · Permutation Combination
The probability that in a random arrangement of the letters of the word 'UNIVERSITY' , the two 'I' s do not come together is
- A \(\frac{1}{5}\)
- B \(\frac{1}{10}\)
- C \(\frac{4}{5}\)
- D \(\frac{3}{10}\)
Answer & Solution
Correct Answer
(C) \(\frac{4}{5}\)
Step-by-step Solution
Detailed explanation
\( P(\text{I's together}) = \frac{9!}{\frac{10!}{2!}} = \frac{9! \times 2}{10!} = \frac{2}{10} = \frac{1}{5} \) \( P(\text{I's not together}) = 1 - P(\text{I's together}) = 1 - \frac{1}{5} = \frac{4}{5} \)
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