The numbers $1, 2, 3,$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. $A$ person draws two slips from the box,one after the other,without replacement. Describe the sample space for the experiment.

Let the first slip drawn be $x$ and the second slip drawn be $y$. Since the slips are drawn without replacement,$x \neq y$.
If the first slip is $1$,the second slip can be $2, 3,$ or $4$. This gives the outcomes $(1, 2), (1, 3), (1, 4)$.
If the first slip is $2$,the second slip can be $1, 3,$ or $4$. This gives the outcomes $(2, 1), (2, 3), (2, 4)$.
If the first slip is $3$,the second slip can be $1, 2,$ or $4$. This gives the outcomes $(3, 1), (3, 2), (3, 4)$.
If the first slip is $4$,the second slip can be $1, 2,$ or $3$. This gives the outcomes $(4, 1), (4, 2), (4, 3)$.
Thus,the sample space $S$ is:
$S = \{(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)\}$