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.
Best Answer
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 $(2^{90}-1)^{100}$.