In an examination hall there are ' $m n$ ' chairs in $m$ rows and $n$ columns. The number of ways in which $m$ students can be seated such that no row is vacant is

Question

In an examination hall there are ' $m n$ ' chairs in $m$ rows and $n$ columns. The number of ways in which $m$ students can be seated such that no row is vacant is, $m^n n$ !, $n^m m$ !, $m^m n !$, $n^n m$ !

MARKS App · Accepted Answer

Given that these is ' $m n$ ' chairs in $m$ rows and $n$ columns. $\therefore$ Number of ways in which one student can seat in Ist column $=n$ So, similarly $m$ students can seat in $n^m$ ways. Since, students can be arranged in $m$ ! ways, $\therefore$ Total number of ways $=m ! \times n^m$ ways

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