Statistics And Probability Question 207
Question: The letter of the word `ASSASSIN’ are written down at random in a row. The probability that no two S occur together is
[BIT Ranchi 1990; IIT 1983]
Options:
A) $ \frac{1}{35} $
B) $ \frac{1}{14} $
C) $ \frac{1}{15} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
-
Total ways of arrangements $ =\frac{8\,!}{2\,!.4\,!} $ $ \bullet \,w\bullet x\bullet y\bullet z\bullet $ Now ?S? can have places at dot?s and in places of $ w,x,y,z $ we have to put $ 2\,A's, $ one $ I $ and one $ N. $ Therefore favourable ways $ =5( \frac{4\,!}{2\,!} ) $ Hence required probability $ =\frac{5\,.\,4\,!2\,!4\,!}{2\,!8\,!}=\frac{1}{14}. $
BETA
