Question

$5$ boys and $3$ girls sit in a row at random. The probability that no two girls sit together is

• A. $\frac{3}{14}$
• B. $\frac{5}{14}$
• C. $\frac{9}{14}$
• D. $\frac{7}{14}$

Answer 1

The correct option is B $\frac{5}{14}$

Total ways of arrangement $=8!$
We can make those 3 girls sit in spaces between boys
No. of such spaces $=5+1=6$
$\Rightarrow P=6C_3\ast 3!\ast 5!/8!=5/14$