Naoko found a deck of playing cards that had been dropped onto the floor. she picked up at least one card. she may have picked up 1, all 52, or any number in between. how many possible combinations of cards might she have picked up?

The answer to this question would be: 2*52! -1

In this case, the card is either picked up by Naoko or they are not picked up. That means there are two possible outcomes for each card. For 52 card, the possibility should be:
2*52!

If Naoko needs to pick at least one, the possibilities become one less because "no card picked" possibility is ruled out