The number of different ways in which $8$ persons can stand in a row so that between two particular persons $A$ and $B$ there are always two persons, is

We will first choose the $2$ people that are between $A$ and $B$ in ${}^6{C}_2$ ways
So, $A\_\_\_\_B$ becomes $1$ unit
This $1$ unit and the $4$ remaining persons can be arranged in $5!$ ways.
$A,B$ and the two people between them can be arranged in $2$ ways each. The total number of arrangements of this one unit is $2\times 2=4$
So the total number of arrangements possible is ${}^6{C}_2\times 5!\times 4=60\times 5!$