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 three different members. There are 15 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 \( \square \) different ways to appoint the four officers. b. How many different ways can a committee of three be appointed? There are \( \square \) different ways to appoint a committee of three. c. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates? P(getting the three youngest of the qualified candidates) = (Type an integer or a simplified fraction.)

1. Andy, Luna, Tia, and Kian all volunteered to participate in the pep rally. a. Make a list or tree diagram to show the sample space if two students will be picked to participate. Andy and Lunu Andy and Tiq Tih and Lunh Andy and Kian Kan anc Lumd b. What is the likelihood that Kian is picked first and Luna is picked second?

\begin{tabular}{l|l} Use your understanding of proll \\ 1. Andy, Luna, Tia, and Kian all volunteered to & \( \begin{array}{l}\text { 2. } \\ \text { participate in the pep rally. } \\ \text { a. Make a list or tree diagram to show the } \\ \text { sample space if two students will be picked } \\ \text { to participate. }\end{array} \) \\ \hline\end{tabular}

(b) If an output component is only accepted when its length lies in the range between 112.8 mm and 168.0 mm , find the expected proportion of components that are accepted. i.e. determine the below probability. Enter your answer rounded correct to 4 decimal places \( P(112.8<X<168.0)= \) Number mm

20. Du kastar två tärningar. Den ena tärningen är fyrsidig där sidorna är numrerade från 1 till 4 . Den andra tärningen är sexsidig där sidorna är numrerade från 1 till 6 . Visa att sannolikheten för att minst en av tärningarna visar en "trea" är \( 3 / 8 \).

1. Andy, Luna, Tia, and Kian all volunteered participate in the pep rally. a. Make a list or tree diagram to show the sample space if two students will be picked to participate. b. What is the likelihood that Kian is picked first and Luna is picked second?