Question

Fifteen persons, among whom are $A$ and $B$, sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$ is

• A. $1/7$
• B. $2/17$
• C. $3/17$
• D. $4/17$

Answer 1

The correct option is A $1/7$

Number of ways we can arrange $15$ persons to sit around a round table$=(15-1)!=14!$

Thus total cases$=\angle 4!$

Fav.cases$={}^{13}{C}_4\angle 4.\angle 2.\angle 9$

$=\frac{\angle 13}{\angle 4\angle 9}\angle 4.\angle 2.\angle 9$

$=13!\times 2!$

Thus probability$=\frac{13!\times 2!}{14!}=\frac{2}{14}$

Thus probability$=\frac{1}{7}$.