Question

When 5-boys and 5-girls sit around a table the probability that no two girls come together

• A. $\frac{1}{120}$
• B. $\frac{1}{126}$
• C. $\frac{3}{47}$
• D. $\frac{4}{7}$

Answer 1

The correct option is B $\frac{1}{126}$

$E\to$ first boys can be arranged in $\angle 4$ ways, then there are 5-gaps between boys in 5-gaps, 5-girls can be arranged in $\angle 5$ ways
$P\left(E\right)=\frac{\angle 5\angle 4}{\angle 9}=\frac{5\times 4\times 3\times 2}{5\times 6\times 7\times 8\times 9}=\frac{1}{126}$