Question

Eight persons numbered $1,2,3,....,8$ to be seated round a circular table at random. The probability that the person numbered $1$ sits between $2$ and $3$ is

• A. $\frac{1}{21}$
• B. $\frac{1}{42}$
• C. $\frac{1}{56}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{1}{21}$

Total ways $=(8-1)!=7!$
Keeping $213$ fixed no. of ways $=(6-1)!=5!$
But $213$ and $312$ both are possible
Therefore, actual probability $=5!\ast 2/7!=1/21$