Explanation

(a)
$\because$ Total number of seats$= n$
and number of people$= m$
Ist person can be seated in $n$ ways
IInd person can be seated in $(n - 1)$ ways
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots\cdots\cdots\cdots\cdots$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots\cdots\cdots\cdots\cdots$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \cdots\cdots\cdots\cdots$
$m$th person can be seated in $(n - m + 1)ways$
$\therefore$ Total number of ways
$= n(n - 1)(n - 2)\ldots(n - m + 1) = {\ ^{n}P}_{m}$
Alternate In out of $n$ seats $m$ people can be seated in ${\ ^{n}P}_{m}$ ways