Question 30

How many subsets of {1, 2, 3 ... 11} contain at least one even integer?

Solution

Total number of subsets that can be formed with the left of 11 elements = $$2^{11}$$ = 2048
The number of subsets which contain only odd numbers(1, 3, 5, 7, 9, 11} = $$2^{6}$$ = 64
Number of subsets which contain at least one even integer = Total number of subsets - the number of subsets which contain only odd numbers
$$\Rightarrow$$ 2048 - 64 = 1984. Hence, option C is the correct answer.

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How many subsets of {1, 2, 3 ... 11} contain at least one even integer?

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