a pharmacist uses 5 separate weights: 1g, 2g,4g,8g and 16g. If the pharmacist can combine these weights to create a new weight, how many different weights are possible?

Answer 1

the 1 g weight can be used in 2 ways, either take it or don't take
the 2g weight can be used in 2 ways, either take it or don't take it
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so there are 2x2x2x2x2 ways to use the weights or 32
but that includes the case where none of the weights are used and all of the weights are used.

So depending on the wording of the question I would subtract 1 for no weights at all,
so there would be 31 ways.