Question

There are $3$ girls & $5$ boys. In how many way they can be arranged so that each girl does not sit with another girl.

Answer 1

Let arrange five boys first

$xBxBxBxBxBx$

we have total six groups when girls can sit but we have to select $3$

$\begin{array}{ccccc}{{}^{6}C}_3& \times & 5!& \times & 3!\\ \uparrow & & \uparrow & & \uparrow \\ selectionofplaceforgirls& & Arrangementofboys& & Arrangementofgirls\end{array}$

$\frac{6\times 5\times 4}{3!}\times 5!\times 3!=14400$