Question

How many subsets containing an even number of elements are there in a set of 97 objects?

Answer 1

You get extract
`2i` objects out of 97 object in this number of ways:

`\displaystyle \binom{97}{2i} = (97!)/((2i)!(97-2i)!)`

So, the number of all possible subsets is

`\displaystyle \binom{97}{0} + \binom{97}{2} + \ldots + \binom{97}{96} = \sum_(i=0)^(48)\binom{97}{2i} = 79228162514264337593543950336`