Chapter 7.3, Problem 16E

The $14$ colleges of interest to a high school senior include $6$ that are expensive (tuition more than $\text{\$}30,000$ per year), $7$ that are far from home (more than $200$ miles away), and $2$ that are both expensive and far from home.

$\left(\text{A}\right)$ If the student decides to attend a college that is not expensive and within $200$ miles of home, how many selections are possible?

$\text{B}$ If the student decides to attend a college that is not expensive and within $200$ miles of home, during his first two years of college, and then will transfer to a college that is to expensive but far from home, how many selections are possible?