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

Solution
follows here:

__Solution:__
{1,2,3,…11}

Odd
integers – 1,4,5,7,9,11 – six in number

Even
integers – 2,4,6,8,10 – five in number

This
is based on Permutations & Combinations- theory of all possible selections.
Check out the following link on this blog for concept:

Number
of all possible selections from the given ‘n’ things = 2

^{n}-1
Number
of all possible sets from the given 11 numbers = 2

^{11}-1
Number
of all possible sets from the given 6 odd-numbers = 2

^{6}-1
∴ Number of all possible sets including at least one even number

= (Number
of all possible sets from all 11 numbers) – (Number of all possible sets from
the 6 odd-numbers)

= (2

^{11}-1) – (2^{6}-1) = 2048-64 = 1984**Answer (3)**
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