The letters of the word UNIVERSITY are arranged at random. What is the probability that the two I's come together?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{1}{5}\)
UNIVERSITY has 10 letters with I repeated twice, so the number of different arrangements is \(\displaystyle \frac{10!}{2!}\). To keep the two I's together, treat II as one block; that leaves 9 units, all different.
All arrangements \(\displaystyle =\frac{10!}{2!}\)
Arrangements with II together \(=9!\)
Probability \(\displaystyle =\frac{9!}{10!/2!}=\frac{9!\times2}{10!}=\frac{2}{10}=\frac{1}{5}\)