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 15 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 different ways to appoint the officers. b. How many different ways can the committee be appointed? There are different ways appoint the committee. 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) =O (Type an integer or a simplified fraction.)

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 15 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 different ways to appoint the officers. b. How many different ways can the committee be appointed? There are different ways appoint the committee. 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) =O (Type an integer or a simplified fraction.)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Question

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 15 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
different ways to appoint the officers.
b. How many different ways can the committee be appointed?
There are
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?
P(getting the four youngest of the qualified candidates)
(Type an integer or a simplified fraction.)

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