Question

$4$ students decide to stand one behind the other. If they have no preference regarding their position, in how many ways can they order themselves in a line?

• A. $256$
• B. $16$
• C. $24$
• D. $120$

Answer 1

The correct option is C $24$

The first position can be filled in $4$ different ways by anyone of the $4$ students.

Following which, the second position can be filled in by anyone of the remaining $3$ students in $3$ different ways, following which the third position can be filled in $2$ different ways; following which, the fourth position can be filled in $1$ way.

Using counting, number of ways to order $4$ students in a line
$=4\times 3\times 2\times 1=24$

Using permutations, number of ways to order $4$ students in a line
$={}^4{P}_4$
$=\frac{4!}{(4-4)!}$
$=\frac{4!}{0!}$
$=4!=4\times 3\times 2\times 1=24$