Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two I's do not come together. Out of the letters in the word ‘UNIVERSITY’, there are two I’s. The number of words in which two I’s are never together is given by \[= \frac{10!}{2} - 9!\]\[ = \frac{10! - 2 \times 9!}{2}\]\[ = \frac{9!\left[ 10 - 2 \right]}{2}\]\[ = \frac{9! \times 8}{2}\] \[ = 9! \times 4\] ∴ Required probability =\[\frac{9! \times 4}{\frac{10!}{2}} = \frac{9! \times 4 \times 2}{10 \times 9!} = \frac{8}{10} = \frac{4}{5}\] Concept: Random Experiments Is there an error in this question or solution? Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now |