The number of ways in which ten candidates $A_1,A_2,A_3,A_4,\cdots ,A_{10}$  can be arranged in a row

“if $A_1\text{and }{A}_2$  are next to each other is”

Consider $A_1,A_2$  as one unit

$\boxed{A_1{A}_2}\boxed{A_3{A}_4\cdots A_{10}}$

1 unit       8 units

Now these 9 units can be arranged in ${}^9{P}_9$  ways

$A_1,A_2$  are arranged among themselves in ${}^2{P}_2$  ways

$\therefore$  Required number of ways ${=}^9{P}_9{.}^2{P}_2=9!2!$