How many groups of objects can you make from 35 objects?

Answer 1

There are 2^35 = 34,359,738,368 possible groups:

1 group with none of the objects in it;

35 groups with 1 object in them;

595 groups with 2 objects in them;

6,545 groups with 3 objects in them;

...

6,545 groups with 32 objects in them;

595 groups with 33 objects in them;

35 groups with 34 objects in them;

1 group with all 35 objects in it.

Answer 2

2 to the power 35, since each of the objects has two options (included, or excluded, from the set you choose).