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1. \({6\choose 4} = 15\) subsets.

2. \({3 \choose 1} = 3\) subsets. We need to select 1 of the 3 remaining elements to be in the subset.

3. \({6 \choose 4} = 15\) subsets. All subsets of cardinality 4 must contain at least one odd number.

4. \({3 \choose 1} = 3\) subsets. Select 1 of the 3 even numbers. The remaining three odd numbers of \(S\) must all be in the set.