There are n seats around a round table numbered 1, 2, 3, ......, n. The number of ways in which m(≤ n) persons can take seats, is

Since the value of $m$ is less than or euqal to $n$, even it is ciruclar permutation, first select $m$ seats from the $n$ seats, this can be arrangd in $n_{C_m}$ ways

These $m$ seats can be arranged among themselves in $m$ seats in $m!$ ways

Therefore, the number of required arrangments is $n_{C_m}·m!=\boxed{n_{P_m}}$