List all the subsets of S. You may use "C" for chocolate, "V" for vanilla, and "M" for mint.

1. {}
2. C
3. V
4. M
5. CV
6. CM
7. VC
8. VM
9. MC
10.MV
11. CVM

Is this correct.

The order of elements in a set does not matter, so

VM and MV, MC and CM, and CV and VC are the same set.
So list those only once to get 8 subsets.

Yes, your list of subsets of set S is correct. However, if you want to make sure you haven't missed any subsets, you can use the following method to systematically generate all possible subsets of set S:

To generate all subsets of a set with n elements, you can use the binary representation of numbers from 0 to 2^n - 1. Each bit in the binary representation of a number corresponds to an element in the set. If the bit is 1, the element is included in the subset; if it is 0, the element is excluded.

In this case, since we have 3 elements (C, V, M), the total number of subsets will be 2^3 = 8. We can represent each subset by a 3-bit binary number, where each bit corresponds to a flavor (in the order C, V, M).

0 (000) corresponds to the empty subset {}
1 (001) corresponds to the subset {M}
2 (010) corresponds to the subset {V}
3 (011) corresponds to the subset {V, M}
4 (100) corresponds to the subset {C}
5 (101) corresponds to the subset {C, M}
6 (110) corresponds to the subset {C, V}
7 (111) corresponds to the subset {C, V, M}

Therefore, the complete list of subsets of set S is:
1. {}
2. {M}
3. {V}
4. {V, M}
5. {C}
6. {C, M}
7. {C, V}
8. {C, V, M}

Your list matches this result, so it is correct.