Probability 1 Question 16

24. If the letters of the word ‘ASSASSIN’ are written down at random in a row, the probability that no two S’s occur together is $1 / 35$.

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Answer:

Correct Answer: 24. False

Solution:

  1. Total number of ways to arrange ‘ASSASSIN’ is $\frac{8 !}{4 ! \cdot 2 !}$.

First we fix the position $\otimes A \otimes A \otimes I \otimes N \otimes$.

Number of ways in which no two S’s occur together

$$ =\frac{4 !}{2 !} \times{ }^{5} C _4 $$

$\therefore$ Required probability $=\frac{4 ! \times 5 \times 4 ! \times 2 !}{2 ! \times 8 !}=\frac{1}{14}$

Hence, it is a false statement.



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