A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). are 12 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below. a. How many different ways can the four officers be appointed? There are 11,880 different ways to appoint the four officers. b. How many different ways can a committee of four be appointed? There are 495 different ways to appoint a committee of four. c. What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates? P(getting the four youngest of the qualified candidates) \( =\square \) (Type an integer or a simplified fraction.)

To find the probability of randomly selecting the four youngest qualified candidates from the pool of twelve, we first need to determine how many ways we can choose four candidates, and then how many of those ways result in selecting the four youngest. **Total combinations of four candidates from twelve (denominator):** We already know that there are 495 different ways to choose any four candidates from the twelve candidates. **Specific combinations for the four youngest (numerator):** There is exactly 1 way to choose the four youngest candidates, as we are selecting the specific set of four individuals. **Calculating the probability:** The probability \( P \) can be computed as: \[ P(\text{getting the four youngest}) = \frac{\text{number of ways to choose the four youngest}}{\text{total ways to choose any four}} = \frac{1}{495} \] So, the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates is: \[ P(getting the four youngest of the qualified candidates) = \frac{1}{495} \]