Determine the sample space for the experiment.
Three marbles are selected from marbles labeled A through D where the marbles are not replaced and the order of selection does not matter.
A) $S = \{ \mathrm { ABC } , \mathrm { ABD } , \mathrm { BCD } \}$
B) $S = \{ \mathrm { ABC } , \mathrm { ABD } , \mathrm { ACD } , \mathrm { BCD } \}$
C) $S = \{ \mathrm { ABC } , \mathrm { BCD } , \mathrm { CDA } \}$
D) $S = \{ \mathrm { ABC } , \mathrm { ABD } , \mathrm { BCD } , \mathrm { CBA } , \mathrm { CDA } \}$
E) $S = \{ \mathrm { ABC } , \mathrm { ABD } , \mathrm { BCD } , \mathrm { CDB } \}$

Question

Quizplus · Accepted Answer

Since the order of selection does not matter and marbles are not replaced, the sample space consists of all combinations of 3 marbles chosen from 4, which is given by $ \binom{4}{3} = 4 $ possible combinations: ABC, ABD, ACD, and BCD.

Determine the Sample Space for the Experiment S={ABC,ABD,BCD}S = \{ \mathrm { ABC } , \mathrm { ABD } , \mathrm { BCD } \}S={ABC,ABD,BCD}

Determine the Sample Space for the Experiment $S = \{ \mathrm { ABC } , \mathrm { ABD } , \mathrm { BCD } \}$