[2020] There are 42 467 328 possible different pickems

For every group, there are 4! possible permutations (4 * 3 * 2 = 24) and there are four different groups so the number of different pickems at group stage is 24⁴ or 331776.

After the group stage, there are 7 different matches with only 2 possible outcomes (Team A wins or Team B wins) so there are 2⁷ or 128 different knockout combinations

Multiplying 331776 * 128 gives 42467328 different pickems

Fun fact: If we made a country where every habitant does a different pickem that country would have roughly the same population as Uganda