SOLUTION: In how many ways may a factory manager assigns one or more of her 7 workers to undergo a screening test?

2 choices for the 1st worker; 1. assign to undergo screening test.
                              2. don't assign to undergo screening test.
2 choices for the 2nd worker; 1. assign to undergo screening test.
                              2. don't assign to undergo screening test.
2 choices for the 3rd worker; 1. assign to undergo screening test.
                              2. don't assign to undergo screening test.
2 choices for the 4th worker; 1. assign to undergo screening test.
                              2. don't assign to undergo screening test.
2 choices for the 5th worker; 1. assign to undergo screening test.
                              2. don't assign to undergo screening test.
2 choices for the 6th worker; 1. assign to undergo screening test.
                              2. don't assign to undergo screening test.
2 choices for the 7th worker; 1. assign to undergo screening test.
                              2. don't assign to undergo screening test.

That's 2*2*2*2*2*2*2 = 27 = 128 ways

But we must subtract 1 from 128 because one of the 128 ways is to
choose not to assign any of the 7 to undergo screening test.  We
must eliminate that 1 case. 

Answer 128 - 1 = 127

Edwin