Question 2 of 15 Step 1 of 1 Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, M for mushrooms, S for shrimp, E for eggs, F for French, and V for vinaigrette.

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To write out the sample space for the given experiment, we need to consider all possible combinations of the choices represented by the letters O, M, S, E, F, and V.

Assuming that each letter represents a different ingredient that can be chosen independently, the sample space will include all possible combinations of these ingredients.

1. **Single Choices**: Each ingredient can be chosen alone:
   - O
   - M
   - S
   - E
   - F
   - V

2. **Combinations of Two Choices**: We can also combine any two ingredients:
   - OM, OS, OE, OF, OV
   - MS, ME, MF, MV
   - SE, SF, SV
   - EF, EV
   - FV

3. **Combinations of Three Choices**: Next, we can combine any three ingredients:
   - OMS, OME, OMF, OMV
   - OSE, OSF, OSV
   - OEF, OEV
   - OFV
   - MSE, MSF, MSV
   - MEF, MEV
   - MFV
   - SEF, SEV
   - SFV
   - EFG

4. **Combinations of Four Choices**: We can also combine any four ingredients:
   - OMSF, OMSV, OMEF, OMEV, OMFV, OSEF, OSEV, OSFV, OEFV
   - MSEF, MSEV, MSFV, MEFV
   - SEFV

5. **Combinations of Five Choices**: We can combine any five ingredients:
   - OMSFE, OMSFV, OMSVE, OMEFV, OMSEF, OMSEV, OMFSV, OSEFV, MSEFV

6. **Combination of All Six Choices**: Finally, we can combine all six ingredients:
   - OMSFEV

Now, we can summarize the sample space $$ S $$ as follows:

$$
S = \{ O, M, S, E, F, V, OM, OS, OE, OF, OV, MS, ME, MF, MV, SE, SF, SV, EF, EV, FV, OMS, OME, OMF, OMV, OSE, OSF, OSV, OEF, OEV, OFV, MSE, MSF, MSV, MEF, MEV, MFV, SEF, SEV, SFV, EFG, OMSF, OMSV, OMEF, OMEV, OMFV, OSEF, OSEV, OSFV, OEFV, MSEF, MSEV, MSFV, MEFV, SEFV, OMSFE, OMSFV, OMSVE, OMEFV, OMSEF, OMSEV, OMFSV, OSEFV, MSEFV, OMSFEV \}
$$

This set includes all possible combinations of the ingredients represented by the letters.
The sample space includes all possible combinations of the ingredients O, M, S, E, F, and V. This includes single choices like O, M, S, E, F, V, as well as combinations of two, three, four, five, and all six ingredients.

Question 2 of 15 Step 1 of 1 Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for olives, M for mushrooms, S for shrimp, E for eggs, F for French, and V for vinaigrette.

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