Question

Jose is applying to college. He receives information on 7 different colleges. He will apply to all of those he likes. He may like none of them, all of them, or any combination of them. How many possibilities are there for the set of colleges that he applies to?

Answer 1

128 posibilities

Explanation:

We have 7 colleges (A,B,C,...,H) which form a set with seven elements.

What you are asking is the number of elements (or cardinality) of the set that contains all possible sets formed by those 7 elements (or the "power set").

It is known that if n is the number of elements of a given set X, then the cardinality of the power set is
`2^n`.

Therefore, there are
`2^7` or 128 possibilities (or elements) for the set of colleges that he applies to.