From a pool of 12 seniors and 10 juniors, a committee of 10 members is to be formed. How many different ways can this committee be chosen if it must include at least one senior?

Explanation

The total number of ways to select any 10 members from 22 individuals (12 seniors + 10 juniors) is C(22, 10). The only group that contains no seniors is the one with all juniors, which can be chosen in C(10, 10) = 1 way. Hence, the number of groups with at least one senior is C(22, 10) - 1.