Ten people, including Fred, are in the Jazz Club. They decide to form a 3-person steering committee. How many possible committees can be formed that do not include Fred? Do you notice a relationship between your answers of the three parts of this problem?
Using my two previous answers.....
Total committees - Total committtees that include Fred = Total committees that don't include Fred
So we have
120 - 36 = 84 committees that don't include Fred
Note this is the same as C(9,3) = choosing any 3 of 9 people that don't include Fred