A.) From a committee of 15 students, in how many ways can a sub-committee of 3 students be selected?
B.) From a committee of 15 students, in how many ways can a chairsperson and then a secretary be elected?
we want to choose 3 people from a group of 15, so the answer is 15 choose 3, or $\displaystyle {15 \choose 3}$
$\displaystyle _{15}P_2 = 15 \cdot 14$, since there are 15 ways to choose the chair, and for each of those ways, there are 14 ways to choose the secretaryB.) From a committee of 15 students, in how many ways can a chairsperson and then a secretary be elected?