Question

The Statistics Survey Centre has a list of 10 undergraduate and 8 graduate students whom are available for short-term survey work. Whenever such work comes in the Centre must hire a graduate student as a supervisor for the survey team. How many ways can the Centre hire a team (that is one or more students) for a job?

Answer 1

Let us first have a look at formula, this is number of ways of selecting zero or more objects out of n objects,

This can be understood as each object has two choices, it can be selected or not selected.
Here there are 18 students, 8 graduates and 10 undergraduates, hence total number of ways of selecting zero or more students = 2^18
But there are some cases when no graduate student is selected, it means we are making teams from the remaining 10 students, that can be done is 2^10 ways.
Thus number of teams when at least one graduate student is selected is 2^18 - 2^10 =  261120.