Question

Louise wants to visit El Paso San Diego Columbus Los Angeles Jacksonville San Antonio Austin and Chicago. If she decides to visit all or some or none of these cities, how many travel options does she have?

Answer 1

There are eight cities on the list.

The number of groups of 2 is (8·7)/2 = 28
The number of groups of 3 is (8·7·6)/(3!) = 56
The number of groups of 4 is (8·7·6·5)/(4!) = 70
The number of groups of 5 is (8·7·6·5·4)/(5!) = 56
The number of groups of 6 is (8·7·6·5·4·3)/(6!) = 28
The number of groups of 7 is (8·7·6·5·4·3·2)/(7!) = 8

So there are (28+56+70+56+28+8) = 246 ways to visit "some" of them.

There's only one way to visit "all" of them, and
there's only one way to visit "none" of them.

So, all together, Louise has 248 travel options.
If she decides to visit Chicago, I will show her a good time.