Question

The students in a class are seated according to their marks in the previous examination.Once, it so happens that four of the students got equal marks and therefore the same rank To decide their seating arrangement, the teacher wants to write down all possible arrangements one in each of separate bits of paper in order to choose one of these by lots. How many bits of paper are required?

Answer 1

We are given that four students got equal marks. On one bit of paper, one arrangement of rank is to be written.

Let the students be named as $P,Q,R$ and $S$.

Now, $P$ can be treated as having rank I in $4$ ways.
$Q$ can be treated as having rank II in $3$ ways.
$R$ can be treated as having rank III in $2$ ways.
$S$ can be treated as having rank IV in $1$ ways.
Therefore, total number of bits of paper required for all arrangement
$=4\times 3\times 2\times 1=24$