You get extract [tex] 2i [/tex] objects out of 97 object in this number of ways:
[tex] \displaystyle \binom{97}{2i} = \dfrac{97!}{(2i)!(97-2i)!} [/tex]
So, the number of all possible subsets is
[tex]\displaystyle \binom{97}{0} + \binom{97}{2} + \ldots + \binom{97}{96} = \sum_{i=0}^{48}\binom{97}{2i} = 79228162514264337593543950336[/tex]
