Question

A party of $23$ people takes their seats at a round table. The odds against two persons sitting together are

• A. $10:1$
• B. $1:11$
• C. $9:10$
• D. None of these

Answer 1

The correct option is A

$10:1$

Explanation for the correct option:

Find the odds against two persons sitting together :

As $23$ people take their seats at a round table, then the total cases $=22!$

Since two-person sit together so, favorable cases $=2x21!$

The probability that the two persons are sitting together

$$\begin{gathered} =\frac{2\times 21!}{22!} \\ =\frac{2}{22} \\ =\frac{1}{11} \end{gathered}$$

The above probability can be written as $\frac{1}{1+10}$

Therefore, the odds in favor and the odds in against $=10:1$

Hence, the correct option is (A).