A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with four different members. There are 14 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below. a. How many different ways can the officers be appointed? There are 24024 different ways to appoint the officers. b. How many different ways can the committee be appointed? There are 1001 different ways to appoint the committee. c. What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates? $\mathrm{P}$ (getting the four youngest of the qualified candidates) = (Type an integer or a simplified fraction.)

Step 1 ：For part a, we need to find the number of ways to appoint 4 officers from 14 candidates. This is a permutation problem because the order of appointment matters (i.e., the position of president is different from CEO, COO, and CFO). The formula for permutations is P(n, r) = n! / (n-r)!, where n is the total number of items, r is the number of items to choose, and '!' denotes factorial. Therefore, there are \(\boxed{24024}\) different ways to appoint the officers.

Step 2 ：For part b, we need to find the number of ways to appoint a committee of 4 members from the remaining candidates. This is a combination problem because the order of appointment does not matter. The formula for combinations is C(n, r) = n! / [r!(n-r)!]. Therefore, there are \(\boxed{1001}\) different ways to appoint the committee.

Step 3 ：For part c, we need to find the probability of randomly selecting the four youngest candidates out of the 14. This is a combination problem because the order of selection does not matter. The probability is given by the formula P(event) = number of favorable outcomes / total number of outcomes. The number of favorable outcomes is the number of ways to choose the 4 youngest candidates, which is C(4, 4) = 1. The total number of outcomes is the number of ways to choose any 4 candidates out of 14, which is C(14, 4). Therefore, the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates is \(\boxed{\frac{1}{1001}}\).