Determine the sample space for the experiment.
Two marbles are selected from marbles labeled A through $\mathrm { E }$ where the marbles are not replaced and the order of selection does not matter.
A) $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CD } \}$
B) $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CD } , \mathrm { CE } , \mathrm { DE } \}$
C) $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { DE } \}$
D) $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CD } , \mathrm { CE } , \mathrm { DE } , \mathrm { DA } , \mathrm { DB } \}$
E) $S = \{ \mathrm { AB } , \mathrm { AC } , \mathrm { AD } , \mathrm { AE } , \mathrm { BC } , \mathrm { BD } , \mathrm { BE } , \mathrm { CA } , \mathrm { CB } , \mathrm { CD } , \mathrm { CE } , \mathrm { DE } \}$

Question

Quizplus · Accepted Answer

There are 5 choices for the first marble and 4 choices for the second marble (since the marbles are not replaced). However, since the order of selection does not matter, we need to divide by 2 to eliminate the duplicate combinations. So the total number of possible combinations is:
$$ \dfrac{5 \times 4}{2} = 10 $$
Therefore, the sample space must have 10 elements, which only option B satisfies.

Determine the Sample Space for the Experiment E\mathrm { E }E

Determine the Sample Space for the Experiment $\mathrm { E }$