100 people choose any number of combinations from a pool of 90 options.

Question

If 100 people can choose any number of combinations from a set of 90 options, where each option can only be selected once, but each person can select any number of options.

Say there is a product sortiment of 90 different products, [a, b, c...]

Each person can choose any combination of products, but can only choose each product once. So for example a person can choose [a] or [a, b, f, g] but not [a, a, c].

Now if 100 people has to make a selection and each selection doesn't affect other peoples selections. How many combinations does this equal?

EDIT: I forgot to add: [a, b, c] and [b, a, c] should count as the same combination.

Answer 1

Each person individually may or may not choose any option, but has to choose at least one option. Thus each person may choose in $2^{90}-1$ ways. Since the choices are independent between people, the answer is $(2^{90}-1)^{100}$.

Answer 2

Look at the power set of the set of all options - that would have $2^{90} - 1$ elements (removing the empty set)

Now, each person can choose any one of these options, hence the total number of ways would be

$$(2^{90}-1)^{100}$$