Statistics And Probability Question 155
Question: The probability that in the random arrangement of the letters of the word ‘UNIVERSITY’ the two I’s does not come together is
Options:
A) $ \frac{4}{5} $
B) 1/5
C) 1/10
D) 9/10
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] Total no. of arrangements of the letters of the word UNIVERSITY is $ \frac{10!}{2!} $ . No. of arrangements when both I?s are together $ =9! $ So. The no. of ways in which 2 I?s do not together $ =\frac{10!}{2!}-9! $
$ \therefore $ Required probability $ =\frac{\frac{10!}{2!}-9!}{\frac{10!}{2!}}=\frac{10!-9!2!}{10!} $ $ =\frac{10\times 9!-9!2!}{10!}=\frac{9![10-2]}{10\times 9!}=\frac{8}{10}=\frac{4}{5} $
BETA
