Question

Find the probability that in a random arrangement of letter of the words "UNIVERSITY" two 'I' do not come together.

• A. $\frac{4}{5}$
• B. $\frac{1}{5}$
• C. $\frac{3}{5}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{4}{5}$

Out of the letters in the word 'UNIVERSITY' two letters 'I' are alike.

$\therefore Numberofpermutations=\frac{10!}{2}$

Number of words in which two 'I' are never together = Total number of words - Number of words in which two 'I' are together

$\frac{10!}{2}-9!=\frac{10!-29!}{2}=\frac{9![10-2]}{2}=\frac{9!8}{2}=9!4$

$\therefore Requiredprobability=\frac{9\ast 4}{10!/2}=\frac{9!8}{10!}$

$=\frac{8}{10}=\frac{4}{5}$