Question

Five boys and three girls are seated at random in a row. Find the probability that no boys sits between two girls.

Answer 1

Determine the probability

There are $5$ boys and $3$ girls .

Therefore total number of people is $8$.

Total number possible seating arrangement is $8!$

Total number of arrangement of $5$ boys and $3$ girls when $3$ girls are consecutive

$=6!·3!$

$\therefore P\left(E\right)=\frac{3!6!}{8!}=\frac{3\times 2\times 1}{7\times 8}=\frac{3}{28}$

Hence, the probability that no boy sits between two girl is $\frac{3}{28}$.